question_answer

The angular depressions of the top and the foot of a chimney as seen from the top of a second chimney, which is 150 m high and standing on the same level as the first are \[\theta \] and \[\varphi \] respectively, then the distance between their tops when \[\tan \theta =\frac{4}{3}\]and \[\tan \varphi =\frac{5}{2}\], is [Pb. CET 2004; IIT 1965]

A) \[\frac{150}{\sqrt{3}}metres\]

B) \[100\sqrt{3}metres\]

C) \[150metres\]

D) \[100metres\]

Correct Answer: D

Solution :

\[d=150\cot \varphi =60m\], Also\[h=60\tan \theta =80m\]. Hence\[x=\sqrt{{{80}^{2}}+{{60}^{2}}}=100m\].