Two opposite sides of a parallelogram each have a length of #9 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #81 #, how long are the other two sides?

Answer 1

Length of the other two sides #a ~~ color (purple)(9.7415)#

Area of parallelogram #A = b * h = b * a sin theta#

Given #A = 81, b = 9, theta = (3pi)/8#

#a = A / ( b * sin theta) = (cancel(81) 9)/ (cancel(9) * sin ((3pi)/8)#

Length of the other two sides #a = 9 / sin ((3pi)/8) ~~ color (purple)(9.7415)#

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides.To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this byTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by usingTo find the lengths of the other two sides of the parallelogram, we canTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using theTo find the lengths of the other two sides of the parallelogram, we can use the formulaTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formulaTo find the lengths of the other two sides of the parallelogram, we can use the formula for the areaTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula forTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product ofTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area ofTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of theTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of aTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and theTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a paralleTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height.To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogramTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since theTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram,To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the heightTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, whichTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height ofTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which isTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a paralleTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given byTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by theTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogramTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the baseTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram isTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the heightTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distanceTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since weTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, weTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81)To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we canTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange theTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can useTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for theTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height HeightTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometryTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height =To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find thisTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, weTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this heightTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angleTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle)To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \thetaTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) =To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). WeTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacentTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formulaTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent sideTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for theTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side /To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area}To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3πTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8)To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{HeightTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) =To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} \To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) = adjacentTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} ]

Given thatTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) = adjacent sideTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} ]

Given that the area isTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) = adjacent side /To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} ]

Given that the area is To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) = adjacent side / To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} ]

Given that the area is 81 andTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) = adjacent side / 9 adjacent sideTo find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} ]

Given that the area is 81 and the base is To find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) = adjacent side / 9 adjacent side = To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} ]

Given that the area is 81 and the base is 9, weTo find the lengths of the other two sides of the parallelogram, we first need to calculate the length of one of the sides. We can do this by using the formula for the area of a parallelogram, which is given by the product of the base and the height. Since we know the area (81) and one of the sides (9), we can rearrange the formula to solve for the height.

Area = Base * Height 81 = 9 * Height Height = 81 / 9 Height = 9

Now that we have the height, we can use trigonometry to find the length of the other side. Since we know one angle of the parallelogram is (3π)/8, we can use the cosine function to find the length of the adjacent side.

cos(angle) = adjacent side / hypotenuse cos((3π)/8) = adjacent side / 9 adjacent side = 9 * cos((3π)/8)

Using a calculator, we find: adjacent side ≈ 6.436

Since the opposite sides of a parallelogram are equal in length, the lengths of the other two sides are both approximately 6.436 units.To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height. Since the height of a parallelogram is the perpendicular distance between the opposite sides, we can use trigonometry to find this height.

Let's denote the length of one of the other two sides of the parallelogram as ( a ) and the angle between this side and the given side of length 9 as ( \theta ). We'll use the formula for the area of a parallelogram:

[ \text{Area} = \text{Base} \times \text{Height} ]

Given that the area is 81 and the base is 9, we can find the height using trigonometry. The height of the parallelogram can be represented as ( 9 \times \sin(\theta) ), where ( \theta = \frac{3\pi}{8} ).

[ 81 = 9 \times 9 \times \sin\left(\frac{3\pi}{8}\right) ]

Solving this equation for ( \sin\left(\frac{3\pi}{8}\right) ), we find:

[ \sin\left(\frac{3\pi}{8}\right) = \frac{81}{81} = 1 ]

Now that we have the sine of the angle, we can find the length of the other two sides using the cosine function:

[ \cos\left(\frac{3\pi}{8}\right) = \frac{a}{9} ]

We already know that ( \cos\left(\frac{3\pi}{8}\right) ) is not a common value, but we can solve it using the identity ( \sin^2(\theta) + \cos^2(\theta) = 1 ) to find ( \cos\left(\frac{3\pi}{8}\right) ).

[ \cos\left(\frac{3\pi}{8}\right) = \sqrt{1 - \sin^2\left(\frac{3\pi}{8}\right)} = \sqrt{1 - 1^2} = \sqrt{0} = 0 ]

So, ( a = 9 \times 0 = 0 ). This means that the other two sides of the parallelogram have a length of 0, which is not possible. Therefore, there might be a mistake in the given information or calculations.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7