The foot of a 20 ft. ladder is 12 ft. from the base of a house. How far up the side of the house does the ladder reach?

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Answer 1 · 2016-03-15T15:32:07

The ladder reaches $16$ feet up the side of the house.

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Let $c$ denote the ladder.
$c = 20$ feet

$b$ denotes distance of the base of the ladder to the house.
$b = 12$ feet.

we are required to calculate the value of $a:$

Using the Pythagoras Theorem:
$c^2= b^2 + a^2$

$20^2= 12^2 + a^2$

$400 = 144 + a^2$

$400 - 144 = a^2$

$a^2 = 256$

$a=sqrt 256$

$a= 16$ feet.