A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.

Let AB be the ladder.

From figure,

In right angle △ ACB,

By pythagoras theorem,

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

⇒ AB² = AC² + BC²

⇒ 13² = AC² + 5²

⇒ 169 = AC² + 25

⇒ AC² = 169 - 25

⇒ AC² = 144

⇒ AC = $\sqrt{144}$ = 12 m.

Hence, the distance of the other end of the ladder from the ground is 12 m.