Question

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

Answer 1

Let AC be the ladder and A be the position of the window which is 8m above the ground.
Now, the ladder is shifted such that its foot is at point D which is 8m away from the wall.
∴ BD = 8m
At this instance, the position of the ladder is DE.
∴ AC = DE
Using Pythagoras theorem in ΔABC,
AC² = AB² + BC²
= (8m)² + (6m)²
= 64m² + 36m²
= 100m²
= (10m)²
∴ AC = DE = 10m
Using Pythagoras theorem in ΔDBE,
BE² = DE² - BD²
⇒ BE² = (10m⁾² - (8m)²
= 100m² - 64m²
= 36m²
= (6m)²
⇒ BE = 6m
Thus, the required height up to which the ladder reaches is 6m above the ground.