A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 4, 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 · 2018-06-10T02:20:41

$color(gray)(" Since " a > b, " but " hat A < hat B, " such a triangle cannot exist."$

$a = 5, hat A = (3pi)/8, b = 4, hat b = (13pi) / 24$

$color(indigo)("THEOREM. A greater angle of a triangle is opposite a greater side."$

$color(indigo)("Let ABC be a triangle in which angle ABC is greater than angle "$

$color(indigo)("BCA; then side AC is also greater than side AB"$

$color(gray)(" Since " a > b, " but " hat A < hat B, " such a triangle cannot exist."$

A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 4, 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?