# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is (pi)/8 and the angle between B and C is  (7pi)/12. What is the area of the triangle?

Jan 12, 2016

Area= 16.90

#### Explanation:

The given triangle is drawn here

A,B,C are the vertices of the triangle. Side A means side opposite angle A, and so on. Sides are otherwise denoted by letters a,b,c Opposite to angles A,B,C.
Angle C would be $\pi - \frac{\pi}{8} - \frac{\pi}{12}$ = 105 degrees.

Area of the triangle is given by the formula $\frac{1}{2} a b S \in C$ = #1/2 (7)(5) sin105 = 16.90