Question

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 1, respectively. The angle between A and C is `(13pi)/24` and the angle between B and C is `(3pi)/8`. What is the area of the triangle?

Answer 1

`sin(pi/12)`

Explanation:

The third angle is `pi - (13pi/24 + 3pi/8) = pi/12`.
The altitude to the side A is 1 X `sin(pi/12) = sin(pi/12)`.
Area = (base X altitude)/2 = (2 X `sin(pi/12))/2 = sin(pi/12)`.