Question
In a triangle ABC, a = 3, b = 5, c = 7. Find the angle opposite to C.
Answer: Option C
:
C
We know from trigonometric ratios of half angles that tanA2=√(s−b)(s−c)(s−a)(s)
Here we need angle opposite to c i.e., C.
Semiperimeter, S=a+b+c2=3+5+72=152
tanC2=√(s−b)(s−a)(s−c)(s)
=√(s−3)(s−5)(s−7)s=√(15−6)(15−10)(2)4(15−14)(152)
=√9(5)15=√3⇒C2=60∘⇒C=120∘
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:
C
We know from trigonometric ratios of half angles that tanA2=√(s−b)(s−c)(s−a)(s)
Here we need angle opposite to c i.e., C.
Semiperimeter, S=a+b+c2=3+5+72=152
tanC2=√(s−b)(s−a)(s−c)(s)
=√(s−3)(s−5)(s−7)s=√(15−6)(15−10)(2)4(15−14)(152)
=√9(5)15=√3⇒C2=60∘⇒C=120∘
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