Question

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
[Hint: Find the hypotenuse of a right triangle having the sides (11 − 6) m = 5 m and 12 m]

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{tops}\mathrm{of}\mathrm{the}\mathrm{poles}\mathrm{is}\mathrm{the}\mathrm{distance}\mathrm{between}\mathrm{points}\mathrm{A}\mathrm{and}\mathrm{B}. \\ \mathrm{We}\mathrm{can}\mathrm{see}\mathrm{from}\mathrm{the}\mathrm{given}\mathrm{figure}\mathrm{that}\mathrm{points}\mathrm{A},\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{form}\mathrm{a}\mathrm{right}\mathrm{triangle},\mathrm{with}\mathrm{AB}\mathrm{as}\mathrm{the}\mathrm{hypotenuse}. \\ \mathrm{On}\mathrm{using}\mathrm{the}\mathrm{Pythagoras}\mathrm{Theorem}\mathrm{in}△\mathrm{ABC},\mathrm{we}\mathrm{get}: \\ (11-6{)}^2+{12}^2={\mathrm{AB}}^2 \\ \Rightarrow 25+144={\mathrm{AB}}^2 \\ \Rightarrow {\mathrm{AB}}^2=169 \\ \Rightarrow \mathrm{AB}=13 \\ \mathrm{Hence},\mathrm{the}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{tops}\mathrm{of}\mathrm{the}\mathrm{poles}\mathrm{is}13\mathrm{m}. \end{gathered}$$