A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4#. If side C has a length of #18 # and the angle between sides B and C is #( 3 pi)/8#, what are the lengths of sides A and B?

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Answer 1 · 2017-09-26T11:13:19

Lengths of sides #A and B# are # 23.52# unit each.

The angle between sides # A and B# is # /_c =pi/4 = 180/4=45^0#

Angle between sides # B and C# is # /_a =(3pi)/8=(3*180)/8=67.5^0#

Angle between sides #C and A# is

#/_b=180-(45+67.5)= 67.5^0 : C =18 # We know by sine rule

#A/sina=B/sinb=C/sinc :. A= C* sina/sinc =18 * sin67.5/sin 45#

#:.A ~~ 23.52(2dp) #, similarly #B= C* sinb/sinc =18 * sin67.5/sin 45#

#:.B ~~ 23.52 (2dp)#. Lengths of #A and B# are # 23.52# unit each. [Ans]