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Question
Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
Solution
We have,
AC = 14 m, DC = 12m and ED = BC = 9m
Construction: Draw EB ⊥ AC
∴ AB = AC – BC = 14 – 9 = 5m
And, EB = DC = 12 m
In ΔABE, by Pythagoras theorem,
AE2 = AB2 + BE2
⇒ AE2 = 52 + 122
⇒ AE2 = 25 + 144 = 169
⇒ AE = `sqrt169` = 13 m
∴ Distance between their tops = 13 m
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