Exam

JEE Main

Year

2012

Date

7 May

Mode

Online

Subject

Mathematics

Chapter

Heights and Distances

JEE Main 2012 · 7 May · Online · Mathematics · Heights and Distances

If two vertical poles 20 ~m and 80 ~m high stand apart on a...

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

Step-by-step solution

We put one pole at origin. $B C=80 \mathrm{~m}, O A=20 \mathrm{~m}$ Line $O C and A B$ intersect at $M$. To find: Length of $M N$. Eqn of $O C: y=\left(\frac{80-0}{a-0}\right) x\Rightarrow y=\frac{80}{a} x$ Eqn of $A B: y=\left(\frac{20-0}{0-a}\right)(x-a)\Rightarrow y=\frac{-20}{a}(x-a)$ At $M:(1)=(2)$$\begin{aligned}& \Rightarrow \quad \frac{80}{a}x=\frac{-20}{a}(x-a) \\ & \Rightarrow \quad \frac{80}{a}x=\frac{-20}{a}x+20 \Rightarrow x=\frac{a}{5}\\ & \therefore \quad y=\frac{80}{a} \times \frac{a}{5}=16 \end{aligned}$$