Question

From the top of a building $60m$ high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower in meters is

• A. $100$
• B. $90$
• C. $120$
• D. $105$

Answer 1

The correct option is C $120$

Let the height of the tower $=hm$

and the distance between building and tower $=am$
Draw horizontal $AC$ parallel to $ED$.
Then $\angle EDA=\angle CAD=x$
Now, in right angled $△AED,$

$\tan x=\frac{60}{a}$

$\Rightarrow a\tan x=60⟶\left(1\right)$

Again, in right angled $△BCA,$

$\tan x=\frac{(h-60)}{a}$

$\Rightarrow a\tan x=h-60⟶\left(2\right)$

From equations $\left(1\right)\&\left(2\right),$ we get

$\Rightarrow h-60=60$

$\Rightarrow h=120$

$\therefore$ Height of tower is $120m$