question_answer

The angle of elevation of the top of pole from the point A on ground be \[\alpha \], where as angle of depression of the foot of pole from the point which is 'b' foot above point A is \[\beta \], then the length of pole is

A) \[b\tan \alpha \cdot \cot \beta \]      

B) \[b(\cot \alpha )\cdot (\tan \beta )\]

C) \[b\tan \alpha \cdot tan\beta \]            

D) \[b\cos \alpha \cdot \cot \beta \]

Correct Answer: A

Solution :

\[\tan \alpha =\frac{h}{x},\tan \beta =\frac{b}{x}\] \[\frac{\tan \alpha }{\tan \beta }=\frac{h}{b}\]         \[\Rightarrow \,h=b\tan \alpha \cdot \cot \beta \]