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 $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $(7 π) 24$ $(7pi)24$ . What is the area of the triangle?

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Answer 1 · 2018-03-26T07:25:51

$Triangle cannot exist with the given measurements$ $color(red)("Triangle cannot exist with the given measurements"$

$a = 6, ˆ A = \frac{7 π}{24}, ˆ B = \frac{17 π}{24}, b = 8$ $a = 6, hat A = (7pi)/24, hat B = (17pi) / 24, b = 8$

Since $ˆ A + ˆ B = \frac{7 π}{24} + \frac{17 π}{24} = π$ $hat A + hat B = (7pi)/24 + (17pi)/24 = pi$ , third angle $ˆ C$ $hat C$ becomes zero .

Hence a triangle cannot exist with the given measurements.

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)/2417π24(17pi)/24 and the angle between B and C is (7pi)24(7π)24 (7pi)24. What is the area of the triangle?