Question

Two poles, 18 m and 13 m high, stand upright in a playground. If their feet are 12 m apart, find the distance between their tops.

Answer 1

Suppose, the two poles are AB and CD, having the length of 18 m and 13 m, respectively.
Distance between them, BD, is equal to 12 m.
We need to find AC.

From C, draw CE$\perp$AB.

AE=AB-EB
= AB-CD (CD = EB)
= 18-13
= 5 cm
EC = BD = 12 m

Now, by Pythagoras theorem in $△AEC$:
$$\begin{gathered} {\mathrm{AC}}^2={\mathrm{AE}}^2+{\mathrm{EC}}^2 \\ \Rightarrow {\mathrm{AC}}^2=5^2+{12}^2 \\ \Rightarrow {\mathrm{AC}}^2=25+144 \\ \Rightarrow {\mathrm{AC}}^2=169 \\ \Rightarrow {\mathrm{AC}}^2={13}^2 \\ \Rightarrow \mathrm{AC}=13 \end{gathered}$$

Hence, the distance between their tops is 13 m.