A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3#. If side C has a length of #1 # and the angle between sides B and C is #( pi)/8#, what are the lengths of sides A and B?

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Answer 1 · 2017-11-25T10:42:37

Length of sides #A and B# are # 0.44 and 1.14 # unit respectively.

Angle between Sides # A and B# is # /_c= pi/3=180/3=60^0#

Angle between Sides # B and C# is # /_a= pi/8=180/8=22.5^0 :.#

Angle between Sides # C and A# is

#/_b= 180-(60+22.5)=97.5^0#

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=1 :. B/sinb=C/sinc# or

#B/sin97.5=1/sin60 or B= 1* (sin97.5/sin60) ~~ 1.14 (2dp) #

Similarly #A/sina=C/sinc # or

#A/sin22.5=1/sin60 or A= 1* (sin22.5/sin60) ~~ 0.44 (2dp) #

The length of sides #A and B# are # 0.44 and 1.14 # unit

respectively. [Ans]