# A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 10, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Apr 10, 2018

Since color(maroon)(a / sin A != b / sin B, " we cannot form a triangle with the given measurements"

#### Explanation:

$a = 12 , b = 10 , \hat{A} = \frac{3 \pi}{8} , \hat{B} = \frac{7 \pi}{24}$

color(crimson)("As per the Law of sines,"

color(crimson)(a / sin A = b / sin B = c / sin C

a / sin A = 12 / sin ((3pi)/8) = color(brown)(12.99

b / sin B = 10 / sin ((7pi) / 24) = color(indigo)(12.6

Since color(maroon)(a / sin A != b / sin B, " we cannot form a triangle with the given measurements"