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Question

If in a triangle ABC ,a=5,b=4 and cos(AB)=3132. then the third side c is equal to

A
3
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B
6
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C
7
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D
9
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Solution

The correct option is B 6
cos(AB)=1tan2AB21+tan2AB23132=1tan2AB21+tan2AB263tan2AB2=1tanAB2=163
Now tanAB2=aba+bcotC2163=545+4cotC2tanC2=639Also cosC=1tan2(C/2)1+tan2(C/2)
=163811+6381=18144=18c2=a2+b22abcosC=25+1625418=36
Hence c=6.

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