Question:
A 13 m long ladder reaches a window of a building 12 m above the ground. Determine the distance of the foot of the ladder from the building.
Solution:
Let AB and AC be the ladder and height of the building.
It is given that:
AB = 13 m and AC = 12 m
We need to find the distance of the foot of the ladder from the building, i.e, BC.
In right-angled triangle ABC, we have:
$A B^{2}=A C^{2}+B C^{2}$
$\Rightarrow B C=\sqrt{13^{2}-12^{2}}$
$=\sqrt{169-144}$
$=\sqrt{25}$
$=5 \mathrm{~m}$
Hence, the distance of the foot of the ladder from the building is 5 m