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 is 6 m.

Answer 1

Let AB be a ladder and B is the window at 8 m above the ground C.
Now, In right triangle ABC
By using Pythagoras theorem, we have
$$\begin{gathered} {\mathrm{AB}}^2={\mathrm{BC}}^2+{\mathrm{CA}}^2 \\ \Rightarrow {10}^2=8^2+{\mathrm{CA}}^2 \\ \Rightarrow {\mathrm{CA}}^2=100-64 \\ \Rightarrow {\mathrm{CA}}^2=36 \\ \Rightarrow \mathrm{CA}=6\mathrm{m} \end{gathered}$$
Hence, the distance of the foot of the ladder from the base of the wall is 6 m.