# A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 6, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (13pi)/24. What is the area of the triangle?

Aug 19, 2016

12

#### Explanation:

The angles in a triangle add up to $\pi$
so the angle between sides A and B is 4$\pi$/24 or $\pi$/6

The area of a triangle is 1/2 x A x B x sin (angle between them)
Or 1/2 x 8 x 6 x sin $\pi$/6

$\pi$/6 or 30 degrees. Draw an equilateral triangle. Cut it in half .
The ratio of the sides is 1;2:sqrt3
Sin 30 =1/2

The area of the triangle is 1/2 x 8 x 6 x 1/2 =12