Question

Two electric poles of equal heights are opposite to each other on either side of a road. Width of a road is 100 m. The angles of elevation observed from a point between two poles on the road to the tops of the poles are 30${}^o$ and 60${}^o$. Find the height of the pole and the distance of that point from each pole.

Answer 1

Given: Width of the road $DC=100$ m
$\angle$s of elevation of the two poles are $30$ ${}^o$ and 60${}^o$.
Find: Height of the pole and the distance of that point from each pole.
Let $DC$ be the width of the road $=100$ m
Let $DT=x$,
$TC=100-x$
In right angled $\Delta$ADT.
$tan\angle ATD=tan{60}^o=\frac{AD}{DT}$
$\sqrt{3}=\frac{AD}{x}$
$\therefore AD=\sqrt{3}x$ .......... (1)
In right angled $\Delta$BCT,
$tan\angle BTC=tan{30}^o=\frac{BC}{TC}$
$\frac{1}{\sqrt{3}}=\frac{BC}{100-x}$
$\therefore BC=\frac{100-x}{\sqrt{3}}$
$AD=BC$
$\sqrt{3}=100-x$