Question

A man stands $9m$ away from a flag-pole. He observes that angle of elevation of the top of the pole is ${28}^o$ and the angle of depression of the bottom of the pole is ${13}^o$. Calculate the height of the pole.

Answer 1

Let $PL$ be the height of the pole and $MN$ be the height of the man.

The angle of elevation of the top of the pole=${28}^o$

and the angle of depression of the bottom of the pole=${13}^o$

According to the question, the man is $9m$ away from the pole.

$NL=MQ=9m$

Now, in right-angled $△PMQ$,

$\tan \theta =\frac{PQ}{MQ}\Rightarrow \tan {28}^o=\frac{PQ}{9}\Rightarrow 0.5317=\frac{PQ}{9}\left(\text{using trigonometric tables}\right)\therefore PQ=4.7853m$

Again, in right-angled $△MQL$,

$\tan {13}^o=\frac{QL}{MQ}\Rightarrow 0.2309=\frac{QL}{9}\left(\text{using trigonometric tables}\right)\therefore QL=2.0781m$

$\therefore$ Height of the pole:

$PL=PQ+QL=(4.7853+2.0781)m=6.8634m=6.86m.$