A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3#. If side C has a length of #2 # and the angle between sides B and C is #( 3 pi)/8#, what are the lengths of sides A and B?

Question

2492 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-16T09:43:04

Lengths of sides #color(brown)(a ~~ 2.13, b = 1.83#

enter image source here

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

Given : #hat A = (3pi) / 8, hat C = pi / 3, c = 2#

#hat B = pi - (3pi)/8 - pi/3 = (7pi)/24#

#a / sin ((3pi)/8) = b / sin ((7pi)/24) = 2 / sin pi/3#

#a = (2 * sin ((3pi)/8) ) / sin (pi/3) ~~ 2.13#

#b = (2 * sin ((7pi)/24) ) / sin (pi/3) ~~ 1.83#