Question

A ladder is placed on a wall such that it is a distance of 5 m from the wall and it operates a window 5 root 3 metre above the ground find the length of led

Answer 1

Lets suppose the wall is a straight line, the window is $5\sqrt{3}$ above the ground.

The ladder is kept 5 m away from the wall.

So this will be a right angled triangle with the wall as the height and distance between the ladder and wall as the base.

Lets suppose the right angle triangle be ΔABC, where m∠B = 90°

AB = Height of the window from the ground = 5√3 meters

BC = Distance between the ladder and the wall = 5 meters

AC = Length of the ladder

Now, we know, by Pythagoras' Theorem,

In a right angled triangle, the square of the length of the opposite to the right angle is the sum of squares of lengths of other two sides.

In ΔABC, m∠B = 90°,

∴AC² = AB² + BC²

∴AC² = (5√3)² + (5)²

∴AC² = 75 + 25

∴AC² = 100

∴AC = 10 meters

∴The length of the ladder will be 10 meters.

Thank you :)