# A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 8, respectively. The angle between A and C is (17pi)/24 and the angle between B and C is  (7pi)24. What is the area of the triangle?

color(red)("Triangle cannot exist with the given measurements"
$a = 6 , \hat{A} = \frac{7 \pi}{24} , \hat{B} = \frac{17 \pi}{24} , b = 8$
Since $\hat{A} + \hat{B} = \frac{7 \pi}{24} + \frac{17 \pi}{24} = \pi$, third angle $\hat{C}$ becomes zero .