Question

The foot of a ladder is 6 m away from a wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its top reach?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{ladder}\mathrm{be}\mathrm{L}\mathrm{m}. \\ \mathrm{By}\mathrm{using}\mathrm{the}\mathrm{Pythagoras}\mathrm{theorem},\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{ladder}. \\ {6}^2+8^2={\mathrm{L}}^2 \\ \Rightarrow {\mathrm{L}}^2=36+64=100 \\ \Rightarrow \mathrm{L}=10 \\ \mathrm{Thus},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{ladder}\mathrm{is}10\mathrm{m}. \end{gathered}$$


$$\begin{gathered} \mathbf{When}\mathbf{}\mathbf{the}\mathbf{}\mathbf{ladder}\mathbf{}\mathbf{is}\mathbf{}\mathbf{shifted}\mathbf{:} \\ \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{ladder}\mathrm{after}\mathrm{it}\mathrm{is}\mathrm{shifted}\mathrm{be}\mathrm{H}\mathrm{m}. \\ \mathrm{By}\mathrm{using}\mathrm{the}\mathrm{Pythagoras}\mathrm{theorem},\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{ladder}\mathrm{after}\mathrm{it}\mathrm{is}\mathrm{shifted}. \\ {8}^2+{\mathrm{H}}^2={10}^2 \\ \Rightarrow {\mathrm{H}}^2=100-64=36 \\ \Rightarrow \mathrm{H}=6 \\ \mathrm{Thus},\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{ladder}\mathrm{is}6\mathrm{m}. \end{gathered}$$