A triangle has sides A,B, and C. If the angle between sides A and B is $(3pi)/4$ , the angle between sides B and C is $pi/12$ , and the length of B is 9, what is the area of the triangle?

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Answer 1 · 2018-05-24T14:32:32

Area of triangle $color(maroon)(A_t = 14.83$ sq units

Given : $hat A = pi/12, hat C = (3pi)/4, b = 9$

$hat B = pi - pi/12 - (3pi)/4 = pi/6$

$a / sin A = b / sin B$

$a = (b sin A) / sin B = (9 * sin (pi/12)) / sin (pi/6)$

$a = 4.66$

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

$A_t = (1/2) * 4.66 * 9 * sin ((3pi)/4)$

$A_t = 14.83$ sq units

A triangle has sides A,B, and C. If the angle between sides A and B is (3pi)/4(3pi)/4, the angle between sides B and C is pi/12pi/12, and the length of B is 9, what is the area of the triangle?