# 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 (13pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Feb 17, 2018

We can not form a triangle

#### Explanation:

$a = 4 , b = 5 , \hat{A} = \frac{3 \pi}{8} , \hat{B} = \frac{13 \pi}{24}$

$\hat{C} = \pi - \frac{3 \pi}{8} - \frac{13 \pi}{24} = \frac{\pi}{12}$

$\frac{a}{\sin} A = \frac{4}{\sin} \left(\frac{3 \pi}{8}\right) = 4.3296$

$\frac{b}{\sin} B = \frac{5}{\sin} \left(\frac{13 \pi}{24}\right) = 5.0431$

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