Question

Two vertical poles $AB=15m$ and $CD=10m$ 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 $P$ above the line $AC$ is :

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

Answer 1

The correct option is D

$6m$

Explanation for the correct option:

The height of $P$:

From the figure,

$$\begin{gathered} \tan \theta =\frac{10}{x}=\frac{h}{x_2} \\ \Rightarrow x_2=\frac{hx}{10} \\ \tan \varphi =\frac{15}{x}=\frac{h}{x_1} \\ \Rightarrow x_1=\frac{hx}{15} \end{gathered}$$

Also, from the figure

$$\begin{gathered} x=x_1+x_2 \\ \Rightarrow x=\frac{hx}{15}+\frac{hx}{10} \\ \Rightarrow 1=\frac{h}{15}+\frac{h}{10} \\ \Rightarrow 1=\frac{10h+15h}{150} \\ \Rightarrow 150=25h \\ \Rightarrow h=6m \end{gathered}$$

The height of $P$ above the line $AC$ is $6m$.

Hence,option D is correct.