Trigonometric Equations Question 310
Question: If the sides of a triangle are p,q and $ \sqrt{p^{2}+pq+q^{2}} $ , then the biggest angle is
[Kerala (Engg.) 2005]
Options:
A) $ \pi /2 $
B) $ 2\pi /3 $
C) $ 5\pi /4 $
D) $ 7\pi /4 $
Show Answer
Answer:
Correct Answer: B
Solution:
- Largest side is $ \sqrt{p^{2}+pq+q^{2}} $ . If largest angle is $ \theta $ , then $ \cos \theta =\frac{p^{2}+q^{2}-p^{2}-pq-q^{2}}{2pq}=-\frac{1}{2}=\cos ( \frac{2\pi }{3} ) $
Þ $ \theta =\frac{2\pi }{3} $ .
BETA
