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?

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Answer 1 · 2018-04-10T03:21:32

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

$a = 12, b = 10, hat A = (3pi)/8, hat B = (7pi)/24$

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

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

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

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

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

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(7pi)/24 and the angle between B and C is (3pi)/8 (3pi)/8. What is the area of the triangle?