Question

Two vertical poles $AB=15$m and $CD=10$m are standing apart on a horizontal ground with points $A$ and $C$ on the ground. If $P$ is the point of intersection of $BC$ and $AD$, then the height of $P$(in m) above the line $AC$ is

• A. $5$
• B. $\frac{20}{3}$
• C. $\frac{10}{3}$
• D. $6$

Answer 1

The correct option is D $6$


Using similar triangle concept, we have
$\tan {\theta }_1=\frac{10}{x}=\frac{H}{x_1}$
$\Rightarrow x_1=\frac{Hx}{10}$
and $\tan {\theta }_2=\frac{15}{x}=\frac{H}{x_2}$
$\Rightarrow x_2=\frac{Hx}{15}$
$\because x_1+x_2=x$
$\Rightarrow \frac{Hx}{10}+\frac{Hx}{15}=x$
$\Rightarrow 15H+10H=150$
$\Rightarrow H=6$m