Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m; find the distance between their tips.

Let AB and CD be two poles of height 6 m and 11 m respectively.

From figure,

ABDE is a rectangle.

∴ AE = BD = 12 m and ED = AB = 6 m.

From figure,

CE = CD - ED = 11 - 6 = 5 m.

In right-angled triangle,

By pythagoras theorem,

⇒ (Hypotenuse)² = (Perpendicular)² + (Base)²

⇒ AC² = CE² + AE²

⇒ AC² = 5² + 12²

⇒ AC² = 25 + 144

⇒ AC² = 169

⇒ AC = $\sqrt{169}$ = 13 m.

Hence, the distance between the tips of two poles is 13 m.