Question

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 4, 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

4 sin `pi`/12 = 1.0353 areal units, nearly.

Explanation:

The third angle = `pi` `-` 13`pi`/24 + 3`pi`/8) = `pi`/12.
The altitude on the side A is B sin `pi`/12.
Area = base X altitude)/2 = (2 X 4 sin `pi`/12) / 2