Question

A vertical pole and a vertical tower are on the same level ground. From the top of the pole, the angle of elevation of the top of the tower is ${60}^o$ and the angle of depression of the foot of the tower is ${30}^o$. Find the height of the tower if the height of the pole is $20m$.

Answer 1

REF.Image.

Let AB be the tower & CD be the

pole

As, given in the question BE = 20 m

$\therefore$ In $△BCE,tan{30}^{\circ }=\frac{20}{CE}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{20}{CE}$

$\therefore CE=20\sqrt{3}$

Now, in $△ACEtan{60}^{\circ }=\frac{h}{CE}$

$\sqrt{3}=\frac{h}{20\sqrt{3}}\Rightarrow h=60$

$\therefore$ Height of tower = 60+20 = 80 m