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 #15 # 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 · 2018-01-12T10:35:07

The length of sides #A and B# are #5.49 and 10.61 # 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#

The sine rule states if #A, B and C# are the lengths of the sides

and opposite angles are #a, b and c# in a triangle, then:

#A/sina = B/sinb=C/sinc ; C=15 :. B/sinb=C/sinc# or

#B/sin30=15/sin135 or B= 15* (sin30/sin135) ~~ 10.61 (2dp)#

Similarly #A/sina=C/sinc # or

#A/sin15=15/sin135 or A= 15* (sin15/sin135) ~~ 5.49 (2dp) #

The length of sides #A and B# are #5.49 and 10.61 # unit

respectively. [Ans]