Question

A ladder of $10m$ long reaches a window$8m$ above the ground. Find the distance of the foot of the ladder from base of the wall.

Answer 1

Step 1: Draw a figure according to the given data.

Here, AB is equal to length of the wall$=8m$

AC is equal to the length of the ladder $=10m$

Step 2: Find the distance of the foot of the ladder from the base of the wall $\mathbf{=}\mathit{B}\mathit{C}$

In right ∆ABC, by Pythagoras theorem

$$\begin{gathered} {\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2 \\ \Rightarrow {\left(10\right)}^2={\left(8\right)}^2+{\left(BC\right)}^2 \\ \Rightarrow 100=64+{\left(BC\right)}^2 \\ \Rightarrow 100–64={\left(BC\right)}^2 \\ \Rightarrow 36={\left(BC\right)}^2 \\ \Rightarrow \surd 36=BC \\ \Rightarrow \surd (6*6)=BC \\ \Rightarrow BC=6m \end{gathered}$$

Hence, the foot of the ladder is at a distance of $6m$ from the base of the wall.