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?

1 Answer
Feb 26, 2016

A = 72(1+sqrt2)

Explanation:

Lets take a look at the triangle.

GeogebraGeogebra

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)