# 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?

Mar 15, 2016

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

#### Explanation:

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.