# A ladder placed 12.5 feet from a building touches a building exactly 30 feet from the ground. What is the length of a ladder?

Apr 14, 2017

See the entire solution process below:

#### Explanation:

Assuming the ground is level horizontally and the building is level vertically, where the ground and building meet is a right triangle. The ladder leaning against the building forms a right triangle so we can use the Pythagorean Theorem to find the length of the ladded.

The Pythagorean Theorem states:

${a}^{2} + {b}^{2} = {c}^{2}$ where $a$ and $b$ and the arms of the triangle and $c$ is the hypotenuse. In this case, the ground and the building are the arms of the right triangle and the ladder is the hypotenuse.

Substituting the values from the problem and solving for $c$ gives:

${12.5}^{2} + {30}^{2} = {c}^{2}$

$156.25 + 900 = {c}^{2}$

$1056.25 = {c}^{2}$

$\sqrt{1056.25} = \sqrt{{c}^{2}}$

$\sqrt{1056.25} = c$

$c = \sqrt{1056.25} = 32.5$

The length of the ladder is $\textcolor{red}{32.5}$ feet