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 $9$ 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 · 2018-02-26T14:24:19

Length of sides $color(brown)(a = 17.3867, b = 12.7279)$

Given : $hat C = pi/6, hat A = (7pi)/12, c = 9$

$hat B = pi - (7pi)/12 - pi / 6 = pi / 4$

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Applying law of sines,

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

$b = (c sin B) / sin C = (9 * sin (pi/4)) / sin (pi/6) = 12.7279$

$a = (b sin A) / sin B = (12.7279 * sin ((7pi)/12)) / sin (pi/4) = 17.3867$

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 9 9 and the angle between sides B and C is (7pi)/12(7pi)/12, what are the lengths of sides A and B?