A triangle has sides A, B, and C. If the angle between sides A and B is $(pi)/8$ , the angle between sides B and C is $(5pi)/6$ , and the length of side B is 19, what is the area of the triangle?

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Answer 1 · 2018-02-17T08:19:00

Area of triangle $A_t = (1/2) a b sin C ~~ ~color(brown)( 264.5996$ sq units

Given $hatC = pi/8, hatA = (5pi)/6, b = 19$

Third angle $hatB = pi - ((5pi)/6 + pi/8) = pi/24$

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$a/sin A = b / sin B = c / sin C$

$a = (19 * sin ((5pi)/6)) / sin (pi/24)~~color(blue)( 72.7823$

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

$=> (1/2) * 19 * 72.7823 * sin((pi/8) ~~color(brown)( 264.5996$

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/8(pi)/8, the angle between sides B and C is (5pi)/6(5pi)/6, and the length of side B is 19, what is the area of the triangle?