# Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #48 #, how long are the other two sides?

Each of the other sides are approximately 6.49 units long.

The area, A of a parallelogram is the product of its base, b, and is height, h:

The length of the other sides, s, can be found using the equation:

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

Let's denote the length of the other two sides of the parallelogram as ( a ) and ( b ). We know that the area of a parallelogram is given by the formula ( \text{Area} = \text{base} \times \text{height} ).

Given that the area of the parallelogram is 48 and one pair of opposite sides has a length of 8, we can find the height of the parallelogram using the formula ( \text{Area} = \text{base} \times \text{height} ). So, ( 48 = 8 \times \text{height} ), which gives us ( \text{height} = 6 ).

Now, let's consider the triangle formed by one side of length 8, the height of 6, and the angle of ( \frac{3\pi}{8} ). We can use trigonometry to find the lengths of the other two sides ( a ) and ( b ).

Using the sine function, we have ( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} ). Plugging in the values, we get ( \sin\left(\frac{3\pi}{8}\right) = \frac{6}{a} ).

Solving for ( a ), we have ( a = \frac{6}{\sin\left(\frac{3\pi}{8}\right)} ). Similarly, for side ( b ), we have ( b = \frac{6}{\sin\left(\frac{5\pi}{8}\right)} ) because the sum of angles in a triangle is ( \pi ) radians, so the third angle would be ( \pi - \frac{3\pi}{8} = \frac{5\pi}{8} ).

Calculating these values gives ( a \approx 8.45 ) and ( b \approx 9.68 ). Therefore, the other two sides of the parallelogram are approximately 8.45 and 9.68 units long.

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

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 opposite sides of a parallelogram are equal in length, the length of one of the other two sides is also 8 units.

Let's denote the length of one of the other two sides as ( s ). Since the area of the parallelogram is 48 square units and the height is 8 units, we can set up the following equation:

[ \text{Area} = \text{Base} \times \text{Height} ] [ 48 = s \times 8 ]

Now, we can solve for ( s ):

[ s = \frac{48}{8} = 6 ]

Therefore, the length of the other two sides of the parallelogram is 6 units each.

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

- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #6 # and sides C and D have a length of # 2 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?
- A rhombus is a quadrilateral that has four congruent sides. How would you prove that the diagonals of a rhombus intersect at a point that is the midpoint of each diagonal?
- Two opposite sides of a parallelogram each have a length of #5 #. If one corner of the parallelogram has an angle of #(5 pi)/8 # and the parallelogram's area is #12 #, how long are the other two sides?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #6 # and sides C and D have a length of # 2 #. If the angle between sides A and C is #pi/3 #, what is the area of the parallelogram?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #4 # and sides C and D have a length of # 4 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7