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 $15$ 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 · 2017-04-11T06:06:57

$A = 28.978$
$B = 21.213$

Angle of $A = (7 pi)/12, C = pi/6$ , therefore angle of $B = pi - (7 pi)/12 -pi/6 = (3 pi)/12$

we use a formulae, $A / sin A = B / sin B = C / sin C$

$A / sin A = C / sin C$

$A / sin ((7 pi)/12) = 15 / sin (pi/6)$

$A = 15 / sin (pi/6) * sin ((7 pi)/12) =15 / 0.5 * 0.966 = 28.978$

$B / sin B = C / sin C$

$B / sin ((3 pi)/12) = 15 / sin (pi/6)$

$B = 15 / sin (pi/6) * sin ((3 pi)/12) = 15/0.5 *0.707= 21.213$

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 15 15 and the angle between sides B and C is (7pi)/12(7pi)/12, what are the lengths of sides A and B?