Question

A triangle has two corners with angles of `pi / 4` and `pi / 2`. If one side of the triangle has a length of `15`, what is the largest possible area of the triangle?

Answer 1

`A = 112.5`

Explanation:

Let `angle A = pi/4`

Let `angle B = pi/2`

Then `angle C = pi - pi/2 - pi/4`

`angle C = pi/4`

Please observe that is this is an isosceles right triangle. If we choose the side that is length 15 to be the side opposite `angle A`, then the side opposite `angle C` must also be length 15 and these sides are the base and the height of the right triangle. Therefore, the area is:

`A = 1/2(15)(15)`

`A = 112.5`