A 10 meter long ladder leans on a wall. The foot of the ladder is 6 meters away from the wall. How high is the top of the ladder?

Open in App

Solution

Let AC be the ladder and AB be the wall.

Given AC = 10 m and BC = 6 m

Now, by using Pythagoras’ Theorem, we have

(AB)² = (AC)² − (BC)²

⇒ (AB)² = (10 m)² − (6 m)²

⇒ (AB)² = (100 − 36) m²

⇒ (AB)² = 64 m²

⇒ AB =

⇒ AB = 8 m

Thus, the top of the ladder is 8 m high.

Suggest Corrections

Similar questions

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

A ladder leans against a wall with its foot 2 metres away from the wall and it makes a 40° angle with the ground. How high is the top of the ladder from the ground?

Q. Question 15
Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

Q. A ladder

5 m

long is leaning against a wall. The foot of the ladder is pulled out along the ground away from the wall at a rate of

2 m / s

. How fast is the height of ladder on the wall decreasing at the instant when the foot of the ladder is

4 m

away from the wall?

Q. A ladder 13 m long leans against a wall. The foot of the ladder is pulled along the ground away from the wall, at the rate of 1.5 m/sec. How fast is the angle θ between the ladder and the ground is changing when the foot of the ladder is 12 m away from the wall.

Join BYJU'S Learning Program

A 10 meter long ladder leans on a wall. The foot of the ladder is 6 meters away from the wall. How high is the top of the ladder?

Let AC be the ladder and AB be the wall. Given AC = 10 m and BC = 6 m Now, by using Pythagoras’ Theorem, we have (AB)2 = (AC)2 − (BC)2 ⇒ (AB)2 = (10 m)2 − (6 m)2 ⇒ (AB)2 = (100 − 36) m2 ⇒ (AB)2 = 64 m2 ⇒ AB = ⇒ AB = 8 m Thus, the top of the ladder is 8 m high.

Let AC be the ladder and AB be the wall.

Given AC = 10 m and BC = 6 m

Now, by using Pythagoras’ Theorem, we have

(AB)² = (AC)² − (BC)²

⇒ (AB)² = (10 m)² − (6 m)²

⇒ (AB)² = (100 − 36) m²

⇒ (AB)² = 64 m²

⇒ AB =

⇒ AB = 8 m

Thus, the top of the ladder is 8 m high.