A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2#. If side C has a length of #28 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2018-08-11T06:43:19

# A=7(sqrt6-sqrt2)~~7(1.0353)=7.2471#.

Let us denote by #/_(B,C)# the angle between sides #B and C#.

Using the Sine-Rule, then, we have,

#A/(sin/_(B,C))=B/(sin(/_C,A))=C/(sin(/_A,B))#.

#:. A/(sin/_(B,C))=C/(sin(/_A,B))#.

#:. A/sin(pi/12)=28/sin(pi/2)=28/1#.

#:. A=28sin(pi/12)=28{(sqrt3-1)/(2sqrt2)}#.

# rArr A=7(sqrt6-sqrt2)~~7(1.0353)=7.2471#.