A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, 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 · 2018-02-17T02:39:35

Since the third angle $ˆ C = 0$ $hatC =0$ , such a triangle can’t exist.

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Given $ˆ ˆ B = \frac{17 π}{24}, ˆ A = \frac{7 π}{24}$ $hat^B = (17pi)/24, hatA = (7pi)/24$

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 $ˆ C = π - π = 0$ $hatC = pi - pi = 0$

Hence, such a triangle can’t exist.

A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is 17π24(17pi)/24 and the angle between B and C is (7π)24 (7pi)24. What is the area of the triangle?