Question

Two poles of heights 8 meters and 15 meters stand upright on the ground. Their feets are 24 meters apart. What is the distance between their tops?

Answer 1

Let AB be the pole of height 8 m and DC be the pole of height 15 m.

Let BC be the distance between the feet of the two poles.

Construction: Draw a line segment AE parallel to BC.

In the given figure, AECB is a rectangle.

AE = BC = 24 m and EC = AB = 8 m

Also, DE = DC − EC = (15 − 8) m = 7 m

Now, by using Pythagoras’ Theorem in ΔAED, we have

(AD)² = (DE)² + (AE)²

⇒ (AD)² = (7 m)² + (24 m)²

⇒ (AD)² = (49 + 576) m²

⇒ (AD)² = 625 m²

⇒ AD =

⇒ AD = 25 m

Thus, the distance between the tops of the two poles is 25 m.