Question

A ladder is placed against a wall such that its foot is at a distance of 5 m from the wall and its top reaches a window 5 root 3 m above the ground.Find the length of the ladder.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{ABC}\mathrm{be}\mathrm{a}\mathrm{right}\mathrm{trangle}.\angle \mathrm{B}={90}^0 \\ \mathrm{Now},\mathrm{let}\mathrm{AC}\mathrm{the}\mathrm{hypotenuse}\mathrm{be}\mathrm{the}\mathrm{ladder}\mathrm{and}\mathrm{AB}\mathrm{the}\mathrm{perpendicular}\mathrm{is}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{window}\mathrm{form}\mathrm{the}\mathrm{ground}. \\ \mathrm{Given},\mathrm{BC}\left(\mathrm{Base}\right)=5\mathrm{m}\mathrm{and}\mathrm{AB}\left(\mathrm{Perpendicular}\right)=5\sqrt{3}\mathrm{m} \\ \mathrm{In}\mathrm{right}\mathrm{angled}\mathrm{triangle}\mathrm{ABC} \\ {\mathrm{AC}}^2={\mathrm{AB}}^2+{\mathrm{BC}}^2 \\ \Rightarrow {\mathrm{AC}}^2={\left(5\sqrt{3}\right)}^2+{\left(5\right)}^2 \\ \Rightarrow {\mathrm{AC}}^2=75+25 \\ \Rightarrow {\mathrm{AC}}^2=100 \\ \Rightarrow \mathrm{AC}=10\mathrm{m} \\ \mathrm{Hence},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{ladder}\mathrm{is}10\mathrm{m}. \end{gathered}$$