A triangle has sides A,B, and C. If the angle between sides A and B is $(pi)/3$ , the angle between sides B and C is $pi/4$ , and the length of B is 5, what is the area of the triangle?

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Answer 1 · 2018-06-03T10:12:05

Area $A_t color(brown)(= 7.92$ sq units

Area of triangle $A_t = (1/2) a b sin C$

Law of Sines $a / sin A = b / sin B = c / sin C$

$hat A = pi/4, hat C = pi/3, hat B = (5pi)/12, b = 5$

$a = (5 * sin (pi/4)) / sin ((5pi)/12) = 3.66$

$A_t= (1/2) * 3.66 * 5 * sin (pi/3) color(brown)(= 7.92$ sq units

A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/3(pi)/3, the angle between sides B and C is pi/4pi/4, and the length of B is 5, what is the area of the triangle?