Question

Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

Answer 1

Let AB be a vertical wall and AC = 10 m is a ladder.

The top of the ladder reaches to A and distance of ladder from the base of the wall BC is 6 m.

In right angled ΔABC,

AC² = AB² + BC²   ...[By pythagoras theorem]

⇒ (10)² = AB² + (6)²

⇒ 100 = AB² + 36

⇒ AB² = 100 – 36 = 64

∴ AB = `sqrt(64)` = 8 cm

Hence, the height of the point on the wall where the top of the ladder reaches is 8 cm.