Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(3pi)/8`, the angle between sides B and C is `(pi)/2`, and the length of B is 12, what is the area of the triangle?

Answer 1

`A = 72(1+sqrt2)`

Explanation:

Lets take a look at the triangle.

The area of a triangle is given by the formula;

`A = 1/2 "base" xx "height"`

The angle `pi/2` is a right angle, so the area of our triangle is;

`A= 1/2 B xx C`

We are given the length of `B`, and we can solve for `C` using the tangent formula.

`tan theta = C/B`

`tan ((3pi)/8) = C/12`

`C = 12 tan ((3pi)/8)`

We can solve for `tan((3pi)/8)` using a calculator or using the half angle formula. Since its not the emphasis of the problem, I'll just include a link to the solution here. The punch line is;

`tan((3pi)/8) = 1+ sqrt(2)`

So our area function becomes;

`A = 1/2 BxxC = 1/2(12)(12(1+sqrt2))`

`A = 72(1+sqrt2)`