question_answer

The angles of elevation of the top of a tower from two points at a distance X and y from the foot of the tower are complementary. The height of the tower is:

A)  \[\sqrt{\frac{x}{y}}\]                            

B)  \[\sqrt{x+y}\]

C)  \[\sqrt{xy}\]                             

D)  \[\frac{x}{y}\]

Correct Answer: C

Solution :

 \[\alpha +\beta =90{}^\circ \]   -(Given) \[\tan \alpha =\frac{h}{y}\]                    ??. (i) \[\tan \beta =\frac{h}{x}\,\,\,\Rightarrow \,\,\tan \,\,(90{}^\circ -\alpha )=\frac{h}{x}\] \[\cot \,\alpha =\frac{h}{x}\]                   ?.. (ii) From equation (i) and (ii), We get,     \[1+xy={{h}^{2}}\Rightarrow h=\sqrt{\mathbf{xy}}\]