Question

The foot of a ladder is placed 5 feet from a building the top of the ladder rests 12 feet up on the building how long is the ladder?

Answer 1

$<b><u><i> Hey mate!! Here's your answer</i></u></b>$
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$\huge{Given}$

The distance between the bottom of a building and foot of a ladder is 5 feet. The height of the building is 12 feet.

$\huge{To\: find}$

The height of the ladder.

$\huge{Solution}$

In the figure attached, let AB be the height of the building and CB be the distance between the foot of ladder and the building.

Now, the building would obviously stand at 90°.

So, this makes a right ∆ABC, where angle B = 90°

Now, side opposite to 90° i.e. AC is the hypotenuse.

Then, by Pythagoras' Theorem, which states that in a right angled triangle, the square of the hypotenuse is equal to the square of other two sides, we get,

AC² = AB² + BC²

=> AC² = 12² + 5²

=> AC² = 144 + 25

=> AC ² = 169

=> AC = √169

=> AC = 13.

So, the height of the ladder -
$\mathcal{\boxed{\bold{\red{=\: AC\:= \: 13\: feet\:}}}}$
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$\huge{\mathcal{\green{Thank\: you}}}$