A triangle has sides A, B, and C. The angle between sides A and B is $(5pi)/6$ . If side C has a length of $16$ and the angle between sides B and C is $pi/12$ , what are the lengths of sides A and B?

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Answer 1 · 2018-04-06T06:39:13

$color(brown)("Lengths of sides " a = b = 8.28$

$"Given : " hat A = pi/12, hat C = (pi)/6, hat B = pi - pi/12 - (5pi)/6 = pi/12, c = 15$

$"To find lengths a, b"$

Since $hat B = hat A$ , it's an isosceles triangle with sides a & b equal.

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

$a = b = (16 * sin (pi/12)) / sin ((5pi)/6) = 32 sin (pi/12) = 8.28$

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6(5pi)/6. If side C has a length of 16 16 and the angle between sides B and C is pi/12pi/12, what are the lengths of sides A and B?