A triangle has sides A, B, and C. If the angle between sides A and B is $(3pi)/8$ , the angle between sides B and C is $(pi)/3$ , and the length of B is 6, what is the area of the triangle?

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Answer 1 · 2018-06-28T02:54:04

$color(crimson)(A_t = (1/2) a b sin C ~~ 18.55 " sq units"$

$hat A = pi/3, hat C = (3pi)/8, hat C = pi - pi/3 - (3pi) / 8 = (7pi) / 24, b = 6$

![ edv-nord.info )

$a = (b sin A) / sin B = (6 * sin (pi/3)) / sin ((7pi)/24) ~~ 6.55$

Formula for area of triangle is $A_t = (1/2) a b sin C$

$color(crimson)(A_t = (1/2) 6.55 * 6 * sin ((3pi) / 8) ~~ 18.55 " sq units"$

A triangle has sides A, B, and C. If the angle between sides A and B is (3pi)/8(3pi)/8, the angle between sides B and C is (pi)/3(pi)/3, and the length of B is 6, what is the area of the triangle?