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Question

Given angle A=60, c=31, b=3+1. Solve the triangle

A
a=6, B=15, C=100
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B
a=6, B=15, C=105
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C
a=12, B=15, C=105
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D
a=6, B=105, C=15
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Solution

The correct option is D a=6, B=105, C=15
A=60B+C=120We know, tanBC2=bcb+ccotA2tanBC2=(3+1)(31)(3+1)(31)cot(602)=223(3)=1BC2=45BC=90B+C=120B=105 and C=15,From sine rule,a=b sinAsinB=3+1(sin60sin105)sin105=sin(60+45)=32(12)+12(12)=3+122a=(3+1)(3)(2)(2)(3+1)2=6a=6, B=105, C=15
Option d is correct.


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