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 #2 # 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 · 2017-07-04T07:50:34

The lengths of the sides are #A=0.88# and #B=2.29#

We apply the sine rule to the triangle #ABC#.

#A/sin hat A=B/sin hat B=C/ sin hatC#

The angle #hat B# is

#=pi-(hatA+hatC)#

#=pi-(1/3pi+1/8pi)=pi-11/24pi=13/24pi#

Therefore,

#A/sin(1/8pi)=B/sin(13/24pi)=2/sin(1/3pi)=2.31#

#A=2.31*sin(1/8pi)=0.88#

#B=2.31*sin(13/24pi)=2.29#