Question

A triangle has two corners with angles of `pi / 2` and `( pi )/ 8`. If one side of the triangle has a length of `13`, what is the largest possible area of the triangle?

Answer 1

The area is `169/(2(sqrt(2)-1))~~204`

Explanation:

If one of the angles of the triangle is `pi/2`, it is a right triangle. The measure of the third angle of the triangle must be `pi/2-pi/8=(3pi)/8`. The shortest side of this right triangle will be the leg that is opposite the angle measuring `pi/8`. Let `x`= the length of the longer leg. The area, `A`, of the triangle will be

`A=13/2x`

From trigonmetry

`x=13/tan(pi/8)`

So

`A=13^2/(2tan(pi/8))=169/(2(sqrt(2)-1))~~204`