A triangle has sides A, B, and C. The angle between sides A and B is #(3pi)/4#. If side C has a length of #24 # and the angle between sides B and C is #pi/12#, what are the lengths of sides A and B?

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Feb 18, 2018

Answer:

Lengths of sides #color(red)(a = 8.7846, b = 16.9706#

Explanation:

Given : #hatA = pi/12, hat C = (3pi)/4, c = 24#

To find #a, b#

Third angle #hat B = pi - (3pi)/4 - pi/12 = pi/6#

By the law of sines,

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

#a = (c * sin A) / sin C = (24 * sin (pi/12)) / sin ((3pi)/4) = color(purple)(8.7846)#

#b = (c * sin B) / sin C = (24 * sin (pi/6)) / sin ((3pi)/4) = color (purple)(16.9706#

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