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 #5 # 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 · 2017-10-01T12:59:22

The lengths of sides #A and B# are # 1.83 ,3.54 # 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=5 :. B/sinb=C/sinc# or

#B/sin30=5/sin135 or B= 5* (sin30/sin135) ~~ 3.54 (2dp) #

Similarly #A/sina=C/sinc # or

#A/sin15=5/sin135 or A= 5* (sin15/sin135) ~~ 1.83 (2dp) #

The length of sides #A and B# are # 1.83 ,3.54 # unit respectively.

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