question_answer

If the perpendicular AD divides the base of the triangle ABC such that BD, CD and AD are in the ratio 2, 3 and 6, then angle A is equal to [MP PET 1993]

A) \[\frac{\pi }{2}\]

B) \[\frac{\pi }{3}\]

C) \[\frac{\pi }{4}\]

D) \[\frac{\pi }{6}\]

Correct Answer: C

Solution :

Obviously, \[\tan A=\frac{\frac{2}{6}+\frac{3}{6}}{1-\frac{2}{6}.\frac{3}{6}}=1\] Þ \[A=\frac{\pi }{4}\]