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

Question

Aicharya · Accepted Answer

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} $

If two vertical poles $20 \mathrm{~m}$ and $80 \mathrm{~m}$ high stand apart on a horizontal plane, then the…

Solution