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 #23 # and the angle between sides B and C is #( 5 pi)/8#, what are the lengths of sides A and B?

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Answer 1 · 2018-05-24T04:24:29

Lengths of sides #color(brown)(a = 42.5, b = 28#

#hat A = (5pi)/8, hat C = pi/6, c = 23#

To find #a, b#

As per Law of Sines,

#a = (c * sin A) / sin C, b = (c * sin B) / sin C#

#hat B = pi - (5pi)/8 - pi/6 = (5pi)/24#

#a = (23 * sin ((5pi)/8)) / sin (pi/6) = 42.5#

#b = (23 * sin (5pi/24) )/ sin (pi/6) = 28#