Question

Two poles of height 12 m and 24 m stand vertically on a plane ground. If the distance between their tops is 13 m. Find the distance between their feet.

Answer 1

Given: Two vertical poles of heights 12 m and 24 m; distance between their tops = 13 m.

Step-wise calculation:

1. Let the distance between their feet = x meters.

2. Place the shorter pole top at 0, 12 and the taller pole top at x, 24.

3. The horizontal separation of the tops equals x and the vertical separation = 24 – 12 = 12.

4. Distance between tops:

`sqrt(x^2 + 12^2) = 13`

So, x² + 144 = 169 

⇒ x² = 25

⇒ x = 5

The distance between their feet is 5 m.