Question

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
(a) $25m$
(b) $50m$
(c) $75m$
(d) $100m$

Answer 1

Correct option is (b). $50m$

Given that: height of cliff is $25m$ and angle of elevation of the tower is equal to angle of depression of foot of the tower that is $\theta$.

Now, the given situation can be represented as,

Here, $D$ is the top of cliff and $BE$ is the tower.

Let $CE=h,AB=x$. Then, $AB=DC=x$

Here, we have to find the height of the tower $BE$.

So, we use trigonometric ratios.

In a triangle $ABD$,

$\Rightarrow \tan \theta =\frac{AD}{AB}$

$\Rightarrow \tan \theta =\frac{25}{x}$ ...(i)

Again in a triangle $DCE$

$\tan \theta =\frac{CE}{CD}$

$\Rightarrow \tan \theta =\frac{h}{x}$

$\Rightarrow \frac{25}{x}=\frac{h}{x}$ [From (i)]

$\therefore h=25$

Thus, height of the tower $=BE=BC+CE=(25+25)m=50m$