Trigonometric Equations Question 264
Question: If the lengths of the sides of a triangle are 3, 5, 7, then the largest angle of the triangle is
[IIT Screening 1994; Kerala (Engg.) 2002]
Options:
A) $ \pi /2 $
B) $ 5\pi /6 $
C) $ 2\pi /3 $
D) $ 3\pi /4 $
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Answer:
Correct Answer: C
Solution:
- Let sides of triangle $ a,b,c $ are respectively 3, 5 and 7.
$ \therefore \cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}=\frac{9+25-49}{2\times 3\times 5} $ $ =\frac{-15}{30}=-\frac{1}{2} $ $ \angle C=\frac{2\pi }{3} $ (largest angle).
BETA
