# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 12, respectively. The angle between A and C is (11pi)/24 and the angle between B and C is  (pi)/24. What is the area of the triangle?

Jun 14, 2017

The area of the triangle is $= 42 {u}^{2}$

#### Explanation:

The angle between $A$ and $B$ is

$\theta = \pi - \left(\frac{11}{24} \pi + \frac{1}{24} \pi\right) = \pi - \frac{12}{24} \pi = \frac{1}{2} \pi$

$\sin \theta = \sin \left(\frac{1}{2} \pi\right) = 1$

The area of the triangle is

$A = \frac{1}{2} A \cdot B \cdot \sin \theta$

$= \frac{1}{2} \cdot 7 \cdot 12 \cdot \sin \left(\frac{\pi}{2}\right)$

$= 42$