A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{17 π}{24}$ $(17pi)/24$ . What is the area of the triangle?

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Answer 1 · 2016-10-11T11:17:18

No such triangle is possible.
As a degenerate form the triangle would have an area of $0$ $0$

The sum of the 3 interior angles must add up to $π$ $pi$ (radians)

$∠ A : C + ∠ B : C = \frac{7 π}{24} + \frac{17 π}{24} = \frac{24 π}{24} = π$ $/_A:C +/_B:C = (7pi)/24+(17pi)/24=(24pi)/24=pi$

$\to ∠ A : B = 0$ $rarr/_A:B=0$

A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is 7π24(7pi)/24 and the angle between B and C is 17π24 (17pi)/24. What is the area of the triangle?