# A triangle has sides A, B, and C. Sides A and B have lengths of 9 and 6, respectively. The angle between A and C is (11pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Jul 21, 2017

The area is $= 13.5 {u}^{2}$

#### Explanation:

The lengths of the sides are

$a = 9$

$b = 6$

The angles are

$\hat{A} = \frac{3}{8} \pi$

$\hat{B} = \frac{11}{24} \pi$

Therefore,

$\hat{C} = \pi - \left(\frac{3}{8} \pi + \frac{11}{24} \pi\right) = \pi - \frac{20}{24} \pi = \frac{1}{6} \pi$

The area of the triangle is

$a r e a = \frac{1}{2} a b \sin \left(\hat{C}\right)$

$= \frac{1}{2} \cdot 9 \cdot 6 + \sin \left(\frac{\pi}{6}\right)$

$= \frac{1}{2} \cdot 9 \cdot 6 \cdot \frac{1}{2} = 13.5 {u}^{2}$