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?

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Answer 1 · 2018-02-17T12:02:22

We can not form a triangle

$a = 4, b = 5, hatA = (3pi)/8, hatB = (13pi)/24$

$hatC = pi - (3pi)/8 - (13pi)/24 = pi/12$

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$a/sin A = 4 / sin ((3pi)/8 )= 4.3296$

$b / sin B = 5 / sin ((13pi)/24) = 5.0431$

Since $a / sin A != b / sin B$ , we cannot form a triangle.

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