Question

From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the height of the pole.

Answer 1

The given information can be represented diagrammatically as:



Here CD is the tower and AB is the pole

In triangle CDB,

$tan60=\frac{CD}{BC}$

$\sqrt{3}=\frac{50}{BC}$

$BC=\frac{50}{\sqrt{3}}$

AE = BC = $\frac{50}{\sqrt{3}}$

In triangle ADE,

$tan45=\frac{DE}{AE}$

$1=\frac{DE}{\frac{50}{\sqrt{3}}}$

$DE=\frac{50}{\sqrt{3}}$

$Thustheheightofthepole=\frac{50}{\sqrt{3}}m$