A ladder $13$ m long rests against a vertical wall. If the foot of the ladder is $5$ m from the foot of the wall, find the distance of the other end of the ladder from the ground in meters.

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Solution

Let BC be the ladder which forms a right angled triangle with the wall.
The distance of the foot of the ladder and the wall, makes AB the base and the distance of the other end of the ladder from the ground, Ac makes the height of the wall.
By Pythagoras theorem, we have $13^{2} = 5^{2} + {A C}^{2}$
$=> {A C}^{2} = 169 - 25 = 144$
$=> A C = 12$ m
So, distance of the other end of the ladder from the ground $= 12$ m.

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