#### Answer

$18.7$ ft.

#### Work Step by Step

In essence, we are looking at a right triangle. The length of the ladder is the hypotenuse. The distance between the base of the ladder and the house is the base of the triangle. The height of the house where the ladder reaches is the height of the triangle, which is what we want to find; we will define this height as $x$.
We can use the Pythagorean theorem to find the height of this right triangle. The Pythagorean theorem is given as:
$a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs of the triangle and $c$ is the length of the hypotenuse.
Let's plug in what we know:
$7^2 + x^2 = 20^2$
Evaluate exponents first:
$49 + x^2 = 400$
Subtract $49$ from both sides of the equation:
$x^2 = 351$
Take the square root of $351$:
$x \approx 18.7$ ft.