# A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 5, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

Jan 12, 2017

$a r e a = 30$

#### Explanation:

First, you would find the third angle:

$\hat{A B} = \pi - \frac{7}{24} \pi - \frac{5}{24} \pi = \frac{12}{24} \pi = \frac{1}{2} \pi$

Well, the triangle is a rectangle triangle!

So you would get the area by simply multiplying the two sides A and B and dividing by 2:

$a r e a = A \cdot B \cdot \frac{1}{2}$

$= {\cancel{12}}^{6} \cdot 5 \cdot \frac{1}{\cancel{2}} = 30$