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.

Answer 1

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