Question

A ladder $5m$long when set against the wall of a house, just reaches a window at a height of $4m$. How far is the foot of the ladder from the wall?

Answer 1

Step 1: Find the distance of the foot of the ladder from the wall

Given, $ladder=5m$ and $heighttoreachwindow=4m$

Let a $△ABC$ such that

$ladderAB=5m$ and $heightAC=4m$

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

We have to find $BC$

By the Pythagoras theorem, in$△ABC$

We have,

$$\begin{gathered} A{C}^2+B{C}^2=A{B}^2 \\ \Rightarrow 4^2+B{C}^2=5^2 \\ \Rightarrow 16+B{C}^2=25 \\ \Rightarrow B{C}^2=25-16=9 \\ \Rightarrow BC=\sqrt{9}=3 \end{gathered}$$

So, $BC=3m$

Hence, the foot of the ladder is $3m$from the wall.