Question

# From the top of a cliff of height $$a$$, the angle of depression of the foot of a certain tower is found to be double the angle of elevation of the top of the tower of height $$h$$. If $$\theta$$ be the angle of elevation then its value is:

A
cos12ha
B
sin12ha
C
sin1a2h
D
tan132ha

Solution

## The correct option is D $$\tan^{-1} \sqrt{3 - \dfrac{2h}{a}}$$h - a = x tan $$\theta$$a = x tan 2$$\theta$$(h - a)/a = $$\dfrac{tan \theta}{tan 2\theta} = \dfrac{1 - tan^2 \theta}{2}$$(h/a) - 1 = $$\dfrac{1 - tan^2 \theta}{2}$$(h/a) - 1 - 1/2 = $$\dfrac{tan^2 \theta}{2}$$$$tan^2\theta$$ = 3 - (2h/a)tan $$\theta$$ = $$\sqrt{3 - (2h/a)}$$$$\theta$$ = $$tan^{-1} \sqrt{3 - \dfrac{2h}{a}}$$Mathematics

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