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Question

In a triangle ABC, a = 3, b = 5, c = 7. Find the angle opposite to C.


A

60

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B

90

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C

120

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D

150

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Solution

The correct option is C

120


We know from trigonometric ratios of half angles that tanA2=(sb)(sc)(sa)(s)
Here we need angle opposite to c i.e., C.
Semiperimeter, S=a+b+c2=3+5+72=152
tanC2=(sb)(sa)(sc)(s)
=(s3)(s5)(s7)s=(156)(1510)(2)4(1514)(152)
=9(5)15=3C2=60C=120


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