From the top of a cliff 25m high, the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is:

25m

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75m

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50m

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100m

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Solution

The correct option is C
50m

In triangle ABE,

$t a n θ_{2} = \frac{A B}{B E} = \frac{25}{B E}$

In triangle ADC,

$t a n θ_{1} = \frac{C D}{A D}$

We know $θ_{1} = θ_{2}$

$\Rightarrow t a n θ_{1} = t a n θ_{2}$

$\frac{C D}{A D} = \frac{25}{B E}$

Since, BE =AD

$\Rightarrow C D = 25$

$\Rightarrow$ Height of tower = CD+ DE (AB)

= 25+25 = 50 m

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