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 $35$ 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 · 2018-03-26T03:10:43

$color(purple)("Lengths of sides " a = b = 18.12 " units"$

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

$hat C = (5pi)/6, hat A = pi/12, c = 35$

$hat B = pi - (5pi)/6 - pi/12 = pi/12$

It's an isosceles triangle with sides a & b equal.

Applying Law of Sines,

$a = b = (c * sin A) / sin C = (35 * sin (pi/12)) / sin ((5pi)/6) = 18.12 "units"$

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 35 35 and the angle between sides B and C is pi/12pi/12, what are the lengths of sides A and B?