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.
Solution:
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:
$A D^{2}=A C^{2}+D C^{2}$
$A D^{2}=5^{2}+12^{2}=25+144=169$
$A D=\sqrt{169}=13 \mathrm{~m}$
Hence, the distance between the tops of the two poles is 13 m.