Question

Two vertical poles of height 9 m and 14 m stand on a plane ground. If the distance between their bases is 12 m, find the distance between their tops.

Answer 1

Let the two poles be DE and AB and the distance between their bases be BE.
We have:
DE = 9 m, AB = 14 m and BE = 12 m
Draw a line parallel to BE from D, meeting AB at C.
Then, DC = 12 m and AC = 5 m
We need to find AD, the distance between their tops.

Applying Pythagoras theorem in right-angled triangle ACD, we have: ​

$$\begin{gathered} A{D}^2=A{C}^2+D{C}^2 \\ A{D}^2=5^2+{12}^2=25+144=169 \\ AD=\sqrt{169}=13\mathrm{m} \end{gathered}$$

Hence, the distance between the tops of the two poles is 13 m.