Question

Two poles of heights $6m$ and $11m$ stand verically on a plane ground. If the distance between their feet is $12m$, what will be the distance between their tops?

• A. $10m$
• B. $12m$
• C. $13m$
• D. $15m$

Answer 1

The correct option is C $13m$

Let the poles be $AB$ and $CD$ as shown in the figure.

$ED=AB=6$

$CD=CE+ED$

$11=CE+6$

$\Rightarrow CE=5$

$AE=BD=12$

Now using pyhagoras theorem in $△AEC$

${\left(AC\right)}^2={\left(CE\right)}^2+{\left(AE\right)}^2{\left(AC\right)}^2={\left(5\right)}^2+{\left(12\right)}^2{\left(AC\right)}^2=25+144=169\Rightarrow AC=\sqrt{169}\Rightarrow AC=13$

So distance between their top is $13m$