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 #19 # 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 · 2018-02-18T13:06:34

Length of side #color(blue)(a = 35.1074)#

Length of side #color(blue)(b = 23.1329)#

#hatA = (5pi)/8, hatC = pi/6, c = 19#

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

#a / sin A = b / sin B = c / sin C#. Law of sines

#a = ((c * sin A) / sin C )= (19 * sin ((5pi)/8) ) / sin (pi/6) = color(green)(35.1074)#

#b = ((c * sin B) / sin C )= (19 * sin( (5pi)/24) ) / sin (pi/6) = color(green)(23.1329)#