Answer
14.1 ft
Work Step by Step
The ladder against the house forms a right triangle against the ground.
The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$.
This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$
The ladder forms the hypotenuse and the distance of the base from the house forms a leg of a right triangle.
You are given the lengths of one leg as 5 and the length of the hypotenuse as 15. Substitute 5 in for a and 15 in for c.
$a^{2}$+$b^{2}$=$c^{2}$
$5^{2}$+$b^{2}$=$15^{2}$
25+$b^{2}$=225
Subtract 25 from both sides.
$b^{2}$=200
Take the square root of both sides to find the length of the missing side.
b=10$\sqrt 2$=14.1
