A triangle has sides A, B, and C. The angle between sides A and B is #pi/4#. If side C has a length of #1 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-07-22T14:26:29

The length of the side #a=0.37#

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The angles are

#hatC=1/4pi#

#hatA=1/12pi#

#hatB=pi-(1/4pi+1/12pi)=pi-(3/12pi+1/12pi)=8/12pi=2/3pi#

The side #c=1#

We apply the sine rule to the triangle

#a/sin hatA=b/sin hatB=c/sin hatC#

#a/sin (1/12pi)=b/sin (2/3pi)=1/sin (1/4pi)#

Therefore,

#a=sin(1/12pi)/sin(1/4pi)=0.37#

#b=sin(2/3pi)/sin(1/4pi)=1.22#