A ladder leans on a wall to reach the height of $ 3.2 \mathrm{~m} $ on the wall. If the length of the ladder is $ 4 \mathrm{~m} $, find the distance of the lower end of the ladder from the base of the wall.

Given: 

A ladder leans on a wall to reach the height of \( 3.2 \mathrm{~m} \) on the wall. 

The length of the ladder is \( 4 \mathrm{~m} \).

To do: 

We have to find the distance of the lower end of the ladder from the wall.

Solution:

Let $AB$ be the ladder and $AC$ be the wall.

$BC$ is be the distance between the wall and the foot of the ladder.

Therefore,

$AB=4\ m$

$AC=3.2\ m$

In $\vartriangle ABC$, using Pythagoras theorem,

$AB^2=AC^2+BC^2$

$\Rightarrow (4)^2=( 3.2)^2+BC^2$

$\Rightarrow 16=10.24+BC^2$

$\Rightarrow BC^2=16-10.24$

$\Rightarrow BC^2=5.76$

$\Rightarrow BC=\sqrt{5.76}$

$\Rightarrow BC=2.4\ m$

The distance between the wall and the foot of the ladder is $2.4\ m$. 

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Updated on: 10-Oct-2022

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