# A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (pi)/24. What is the area of the triangle?

Apr 15, 2016

Area of triangle is $1.449$ units.

#### Explanation:

The formula for area of a triangle given two sides $a$ and $b$ and included angle $\theta$ is $\frac{1}{2} \times a b \times \sin \theta$.

Here, though we have been given two sides as $1$ and $3$, included angle has not been given.

But as other two angles are $\frac{13 \pi}{24}$ and $\frac{\pi}{24}$, third angle will be given by

$\pi - \frac{13 \pi}{24} - \frac{\pi}{24} = \frac{24 \pi - 13 \pi - \pi}{24} = \frac{10 \pi}{24}$

Hence area of triangle is $\frac{1}{2} \times 1 \times 3 \times \sin \left(\frac{10 \pi}{24}\right)$

= $\frac{3}{2} \times 0.9659 = 1.449$ units.