# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (5pi)/8. What is the area of the triangle?

Feb 17, 2018

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

#### Explanation:

Given : $a = 7 , b = 5 , \hat{A} = \frac{5 \pi}{8} , \hat{B} = \frac{7 \pi}{24}$

$\hat{C} = \pi - \left(\frac{5 \pi}{8} + \frac{7 \pi}{24}\right) = \frac{\pi}{12}$

a / sin A = 7 / sin ((5pi)/8 = 7.5767

$\frac{b}{\sin} B = \frac{5}{\sin} \left(\frac{7 \pi}{24}\right) = 6.3024$

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