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  4. Two vertical poles A B=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 :

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Q. Two vertical poles $A B=15 m$ 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 :

JEE MainJEE Main 2020Trigonometric Functions

Solution:

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$\tan \theta=\frac{10}{x}=\frac{h}{x_{2}}$
$ \Rightarrow x_{2}=\frac{h x}{10}$
$\tan \phi=\frac{15}{x}=\frac{h}{x_{1}} $
$\Rightarrow x_{1}=\frac{h x}{15}$
Now, $x_{1}+x_{2}=x=\frac{h x}{15}+\frac{h x}{10}$
$\Rightarrow 1=\frac{h}{10}+\frac{h}{15}$
$ \Rightarrow h=6$