A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/6$ . If side C has a length of $2$ and the angle between sides B and C is $(7pi)/12$ , what are the lengths of sides A and B?

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Answer 1 · 2018-03-28T09:55:55

$color(brown)(a = 3.86, b = 2.828$

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$hat A = (7pi)/12, hat C = pi/6, hat B = pi - (7pi)/12 - pi/6 = pi/4, c = 2$

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

$a = (c * sin A) / sin C = (2 * sin ((7pi)/12))/ sin (pi/6) = 3.86$

$b = (c * sin B) / sin C = (2 * sin (pi/4)) / sin (pi/6) = 2.828$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/6(pi)/6. If side C has a length of 2 2 and the angle between sides B and C is (7pi)/12(7pi)/12, what are the lengths of sides A and B?