Question

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is `(7pi)/24` and the angle between B and C is `(pi)/8`. What is the area of the triangle?

Answer 1

`5(sqrt3+1)/(4sqrt2)` areal units = 0.9859 areal units, nearly..

Explanation:

Using the sum of the angles is `pi`, the third angle between side A and B is `7pi/12`.
The area is `1/2ABsin(angle between A and B)`
`sin(7pi/12) = sin(pi/3+pi/4)`
Expand for the surd...