# A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is (3pi)/8 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

Feb 21, 2016

area ≈ 9.66 square units

#### Explanation:

The area of the triangle can be found using $\frac{1}{2} A B \sin \theta$
where $\theta \text{ is the angle between A and B.}$

since the sum of the 3 angles in a triangle is $\pi$

Then the angle $\theta = \pi - \left(\frac{3 \pi}{8} + \frac{5 \pi}{24}\right)$

$\Rightarrow \theta = \pi - \frac{7 \pi}{12} = \frac{5 \pi}{12}$

rArr "area " = 1/2 xx 4 xx 5 xx sin((5pi)/12) ≈ 9.66