Two poles of heights $6m$and $11m$ stand on a plane ground. If the distance between the feet of the poles is $12m$, find the distance between their tops.
Answer
385.8k+ views
Hint- This question can be solved by using Pythagoras theorem.
It is given that
Height of the first pole is $AB = 6m$
Height of the second pole is $CD = 11m$
Distance between the feet of poles is $AC = 12m$
We have to find the distance between the tops of pole, i.e. $BD$
Let us draw a line $BE \bot DC$
Since, it is clear from the figure that $AC \bot DC$ as pole is vertical to ground.
So, $BE = AC = 12m$
Similarly, $AB = EC = 6m$
Now,
$
DE = DC - EC \\
DE = 11 - 6 \\
DE = 5m \\
$
It is clear from the figure that the angle$\angle BED$ , is ${90^ \circ }$ because$BE \bot DC$
Thus, the triangle $BED$ is a right angled triangle.
By using Pythagoras theorem in the right angle triangle.
$
{\left( {hyp} \right)^2} = {\left( {base} \right)^2} + {\left( {height} \right)^2} \\
\Rightarrow {\left( {BD} \right)^2} = {5^2} + {12^2} \\
{\text{or }}{\left( {BD} \right)^2} = 25 + 144 \\
{\text{or }}{\left( {BD} \right)^2} = 169 \\
{\text{or }}BD = \sqrt {169} \\
BD = 13m \\
$
Hence, the distance between the tops of the pole is $13m$.
Note- Whenever we face such types of questions the key concept is that we should draw its figure and then analyze from the figure what we have to find. Like in this question we find the distance between the two poles from their tops by using Pythagoras theorem.

It is given that
Height of the first pole is $AB = 6m$
Height of the second pole is $CD = 11m$
Distance between the feet of poles is $AC = 12m$
We have to find the distance between the tops of pole, i.e. $BD$
Let us draw a line $BE \bot DC$
Since, it is clear from the figure that $AC \bot DC$ as pole is vertical to ground.
So, $BE = AC = 12m$
Similarly, $AB = EC = 6m$
Now,
$
DE = DC - EC \\
DE = 11 - 6 \\
DE = 5m \\
$
It is clear from the figure that the angle$\angle BED$ , is ${90^ \circ }$ because$BE \bot DC$
Thus, the triangle $BED$ is a right angled triangle.
By using Pythagoras theorem in the right angle triangle.
$
{\left( {hyp} \right)^2} = {\left( {base} \right)^2} + {\left( {height} \right)^2} \\
\Rightarrow {\left( {BD} \right)^2} = {5^2} + {12^2} \\
{\text{or }}{\left( {BD} \right)^2} = 25 + 144 \\
{\text{or }}{\left( {BD} \right)^2} = 169 \\
{\text{or }}BD = \sqrt {169} \\
BD = 13m \\
$
Hence, the distance between the tops of the pole is $13m$.
Note- Whenever we face such types of questions the key concept is that we should draw its figure and then analyze from the figure what we have to find. Like in this question we find the distance between the two poles from their tops by using Pythagoras theorem.
Recently Updated Pages
Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

State the laws of reflection of light

What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE

Explain zero factorial class 11 maths CBSE

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Proton was discovered by A Thomson B Rutherford C Chadwick class 11 chemistry CBSE

What is spore formation class 11 biology CBSE

Can anyone list 10 advantages and disadvantages of friction

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main
