A ladder 10 m long reaches the window of a house 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Question

Philoid · Accepted Answer

Given: Height of the window from the ground = 8 m

Length of the ladder = 10 m

To find: Distance of the foot of the ladder from the base of the wall.

Consider the following diagram corresponding to the question.

Here, AB = Height of the window form the ground = 8 m

AC = Length of the ladder = 10 m

BC = Distance of the foot of the ladder from the base of the wall

Now, in ∆ ABC,

By Pythagoras theorem, we have

AC² = AB² + BC²

⇒ BC² = AC² – AB²

⇒ BC² = (10)² – (8)² = 100 – 64 = 36

⇒ BC = √36 = 6 m