# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 4, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (11pi)/24. What is the area of the triangle?

Feb 17, 2018

We can not form a triangle.

#### Explanation:

$\hat{C} = \pi - \frac{11 \pi}{24} - \frac{5 \pi}{24} = \frac{\pi}{3}$

$\frac{a}{\sin} A = \frac{5}{\sin} \left(\frac{11 \pi}{24}\right) = 5.0431$

$\frac{b}{\sin} B = \frac{4}{\sin} \left(\frac{5 \pi}{24}\right) = 6.5707$

Since $\frac{a}{\sin} A \ne \frac{b}{\sin} B$, we cannot form a triangle.