# A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (pi)/8. What is the area of the triangle?

Jul 14, 2016

Area of the triangle$= 7 \sqrt{3} \cong 12.1247 s q . u n i t .$

#### Explanation:

We note that the third angle of the triangle $= \pi - 13 \frac{\pi}{24} - \frac{\pi}{8} = \left(24 - 13 - 3\right) \frac{\pi}{24} = 8 \frac{\pi}{24} = \frac{\pi}{3}$.

This is the angle btwn. sides A &B

Now, by Trigo., area of the triangle=1/2*A*B*sin (/_(A,B)
$= \frac{1}{2} \cdot 4 \cdot 7 \cdot \sin \left(\frac{\pi}{3}\right) = \frac{1}{2} \cdot 4 \cdot 7 \cdot \frac{\sqrt{3}}{2} = 7 \sqrt{3} \cong 7 \cdot \left(1.7321\right) = 12.1247$ sq.unit.