A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 6 #. If one side of the triangle has a length of #16 #, what is the largest possible area of the triangle?
Largest possible area of the triangle is
Given : Third angle To get the longest area, length 16 should correspond to least angle Area of triangle
By signing up, you agree to our Terms of Service and Privacy Policy
To find the largest possible area of the triangle, you can use the formula for the area of a triangle, which is 0.5 * base * height. Since one side of the triangle is given as 16 units, you need to find the height corresponding to this base. You can use trigonometric ratios to find the height.
Given that one angle of the triangle is (3π)/4 and the adjacent side (base) is 16 units, you can use the cosine ratio (cos) to find the height.
The cosine of an angle is equal to the adjacent side divided by the hypotenuse. So, cos(angle) = adjacent side / hypotenuse.
Therefore, cos((3π)/4) = 16 / hypotenuse.
Solving for the hypotenuse, you get hypotenuse = 16 / cos((3π)/4).
Similarly, for the other angle, you can use the sine ratio (sin) to find the height.
The sine of an angle is equal to the opposite side divided by the hypotenuse. So, sin(angle) = opposite side / hypotenuse.
Therefore, sin(π/6) = height / hypotenuse.
Solving for the hypotenuse, you get hypotenuse = height / sin(π/6).
Now, you have expressions for the hypotenuse in terms of the base and the height. You can substitute these expressions into the formula for the area of the triangle and find the maximum area.
After calculating, you will find that the largest possible area of the triangle is 64√3 square units.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
- Two corners of an isosceles triangle are at #(2 ,9 )# and #(7 ,5 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?
- A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #1 # and #4 # and the pyramid's height is #2 #. If one of the base's corners has an angle of #(5pi)/6#, what is the pyramid's surface area?
- A cone has a height of #27 cm# and its base has a radius of #12 cm#. If the cone is horizontally cut into two segments #4 cm# from the base, what would the surface area of the bottom segment be?
- A cone has a height of #6 cm# and its base has a radius of #4 cm#. If the cone is horizontally cut into two segments #5 cm# from the base, what would the surface area of the bottom segment be?
- Calculate the perimeter of a parallelogram with sides 6 3/4 inches and 5 1/2 inches?

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