Question

If two vertical poles $20m$ and $80m$ high stand apart on a horizontal plane, then the height (in $m$ ) of the point of intersection of the lines joining the top of each pole to the foot of other is

• A. $16$
• B. $18$
• C. $50$
• D. $15$

Answer 1

Answer: (A)

We put one pole at origin.
$BC=80m,OA=20m$
Line $OC$ and $AB$ intersect at $M$ .
To find: Length of $MN$ .
Eqn of $OC:y=\left(\frac{80 - 0}{a - 0}\right)x$
$\Rightarrow y=\frac{80}{a}x$
Eqn of $AB:y=\left(\frac{20 - 0}{0 - a}\right)\left(\right.x-a\left.\right)$
$\Rightarrow y=\frac{- 20}{a}\left(\right.x-a\left.\right)$
At $M:\left(\right.1\left.\right)=\left(\right.2\left.\right)$
$\Rightarrow \frac{80}{a}x=\frac{- 20}{a}\left(\right.x-a\left.\right)$
$\Rightarrow \frac{80}{a}x=\frac{- 20}{a}x+20\Rightarrow x=\frac{a}{5}$
$\therefore y=\frac{80}{a}\times \frac{a}{5}=16$