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 (7pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Feb 5, 2016

15.155

Explanation:

Given is Angle A=$\frac{3 \pi}{8}$ and B=$\frac{7 \pi}{24}$, and side a =7, b =5
The angle between sides a and b would be C= $\pi - \frac{3 \pi}{8} - \frac{7 \pi}{24} = \frac{2 \pi}{3}$

The area of the triangle would be

$\frac{1}{2} a b S \in C$ = $\frac{1}{2}$ (35) Sin $\frac{2 \pi}{3}$

=$\frac{1}{2}$(35) sin $\frac{\pi}{3}$ = $\frac{1}{2} \left(35\right) \frac{\sqrt{3}}{2}$= 15.155