A) \[\frac{\pi }{2}\]
B) \[\frac{5\pi }{4}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{7\pi }{4}\]
E) \[\frac{5\pi }{3}\]
Correct Answer: C
Solution :
The longest side of triangle is\[\sqrt{{{p}^{2}}+{{q}^{2}}+pq}\]. Greatest angle will be opposite to longest side. Let\[\theta \]be greatest angle, then \[\cos \theta =\frac{{{p}^{2}}+{{q}^{2}}-{{p}^{2}}-{{q}^{2}}-pq}{2pq}=-\frac{1}{2}\] \[\Rightarrow \] \[\cos \theta =\cos \frac{2\pi }{3}\] \[\Rightarrow \] \[\theta =\frac{2\pi }{3}\]
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