Two poles of height 9 m and 14 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

Let AB be the smaller pole and CD the bigger pole.

From figure,

⇒ CE = AB = 9 m and AE = BC = 12 m

⇒ CD = CE + ED

⇒ 14 = 9 + ED

⇒ ED = 14 - 9

⇒ ED = 5 m

From figure,

△ADE is right angled triangle.

By pythagoras theorem,

Hypotenuse² = Base² + Height²

⇒ AD² = AE² + ED²

⇒ AD² = (12)² + (5)²

⇒ AD² = 144 + 25

⇒ AD² = 169

⇒ AD = $\sqrt{169}$

⇒ AD = 13 m.

Hence, the distance between their tops is 13 m.