A triangle has sides A, B, and C. The angle between sides A and B is $(7pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 6, what is the area of the triangle?

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Answer 1 · 2018-03-16T06:58:18

$color(red)(A_t ~~ 5.2$ sq units

Given : $hat C = (7pi) / 12, hat A = pi/12, hat B = pi - (7pi)/12 - pi/12 = pi / 3, b = 6$

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$a / sin (pi/12) = 6 / sin (pi/3) = c / sin ((7pi)/12)$

$a = ( 6 * sin (pi/12)) / sin (pi/3) ~~ 1.79$

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Area $A_t = (1/2) a b sin C = (1/2) * 1.79 * 6 sin ((7pi)/12)$

$A_t ~~ 5.2$ sq units

A triangle has sides A, B, and C. The angle between sides A and B is (7pi)/12(7pi)/12 and the angle between sides B and C is pi/12pi/12. If side B has a length of 6, what is the area of the triangle?