Question

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

Answer 1

Let the ladder be AB and BC be the height of the window from the ground.


We have:
AB = 10 m and BC = 8 m
Applying Pythagoras theorem in right-angled triangle ACB, we have:

$$\begin{gathered} A{B}^2=A{C}^2+B{C}^2 \\ \Rightarrow A{C}^2=A{B}^2-B{C}^2={10}^2-8^2=100-64=36 \\ \Rightarrow AC=6\mathrm{m} \end{gathered}$$

Hence, the foot of the ladder is 6 m away from the base of the wall.