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 #2 # 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 · 2018-02-18T16:19:28

Length of side #color(blue)(a = 3.6955, b = 2.435)#

#hatC = pi/6, hatA = (5pi)/8, c = 2#

To find sides a, b

#hatB = pi - (5pi)/8 - pi/6 = (5pi)/24#

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

#a = (c sin A) / sin C = (2 sin ((5pi)/8)) / sin (pi/6) = 3.6955#

#b = (c sin B) / sin C= (2 * sin ((5pi)/24) ) / sin (pi/6) = 2.435#