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 #27 # 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 · 2018-05-24T05:27:58

Lengths of sides #color(crimson)(a = b = 2.7# units

#hat A = pi/12, hat C = (5pi)/6, c = 27, a = ?, b = ?#

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

It’s an isosceles triangle with sides a & b equal as angles are equal.

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

#a = b = (c sin A ) / sin C = (27 * sin (pi/12)) / sin ((5pi)/6)#

#color(crimson)(a = b = 2.7# units