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.

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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:

$A B^{2} = A C^{2} + B C^{2} \Rightarrow B C = \sqrt{13^{2} - 12^{2}} = \sqrt{169 - 144} = \sqrt{25} = 5 m$

Hence, the distance of the foot of the ladder from the building is 5 m

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