Question

Two poles of height $6m$ and $11m$ stand on a plane ground of the distance between their feet $12m$, find the distance between their tops.

Answer 1

Making a figure according to the given question.

Suppose $AB$ and $CD$ are two poles of $11m$ and $6m$ respectively.

We have to find the distance between $B$ and $D$.

Let the distance $BD$ be $xcm$

Join $ED$, such that $∆BED$ is a right angle triangle.

Now, applying Pythagoras theorem, we have;

$$\begin{gathered} Hypotenus{e}^2=Perpendicula{r}^2+Bas{e}^2 \\ B{D}^2=B{E}^2+E{D}^2 \\ {x}^2=5^2+{12}^2 \\ {x}^2=25+144 \\ {x}^2=169 \\ x=\sqrt{169} \\ x=13 \end{gathered}$$

Hence, the distance between the tops of two poles is $13cm$