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 #2 # and the angle between sides B and C is #pi/12#, what are the lengths of sides A and B?

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Answer 1 · 2017-09-21T11:45:20

Length of sides #A and B# are # 0.73 , 1.41# unit respectively.

Angle between sides #A and B# is #/_c=(3pi)/4=(3*180)/4=135^0#

Angle between sides #B and C# is #/_a=pi/12=180/12=15^0 :.#

Angle between sides #C and A# is #/_b=180-(135+15)=30^0 #

Length of side #C=2# ; We know from sine law ,

#A/sin a = B/sin b = C/sin c :. B/sin30 = 2/sin135#

#:. B= 2* sin30/sin135 or B ~~ 1.41# unit, similarly ,

#A/sin15 = 2/sin135 :. A = 2* sin15/sin135 or A ~~ 0.73# unit.

Length of sides #A and B# are # 0.73 , 1.41# unit respectively. [Ans]