Question

The foot of a ladder is 6 m away from a wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its tip reach?

Answer 1

The given information can be represented as follows.

Here, A is the position of the window and AC is the ladder.

Also, DE is the same ladder when it is shifted.

C and E are the original and final position of the foot of the ladder.

Now, applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

⇒ AC² = (8 m)² + (6 m)² = (10 m)²

⇒ AC = 10 m

Now, again applying Pythagoras theorem in ΔEBD

DE² = EB² + BD²

⇒ (10 m)² = (8 m)² + BD²

⇒ BD² = 100 m² − 64 m² = 36 m²

⇒ BD = 6 m

Thus, the tip of the ladder is now at the height of 6 m above the ground.