A building is 2 ft from aa 9-ft fence that surrounds the property. A worker wants to wash a window in the building 13 ft from the ground.ground. He plans to place a ladder over the fence so it rests against the building. (See the figure.) He decides he should place the ladder 9 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?

The length of a missing side length of a right triangle when given the side lengths of the other two can be found using the Pythagorean Theorem or,

[tex]a^2+b^2=c^2[/tex], where a and b are the legs of the triangle and c is the hypotenuse.

This can be rearranged to find the length of a hypotenuse or a leg. It'll look like this,

[tex]a=\sqrt{c^2-b^2}[/tex] or [tex]b=\sqrt{c^2-a^2}[/tex]

and,

[tex]c=\sqrt{a^2+b^2}[/tex].

Applying the Theorem

In this problem, drawing an image depicting what's going on is best to understand the questions that's being asked.

A window on a building that's 13 feet in height is trying to be reached by a ladder. So, knowing that a right angle is formed between the building and the ground, which verifies that this is a right triangle problem, we know that the vertical leg of the triangle is 13 feet in length.

After the worker finally determines where he will place the ladder on the ground, we can calculate the horizontal leg length by summing the distance between the building/window to the fence and the distance between the fence and the position of the ladder.

So, the horizontal leg is 2 + 9 or 11 feet in length.

The problem asks for the length of the ladder so, the hypotenuse or, c needs to be calculated.

Using [tex]c=\sqrt{a^2+b^2}[/tex] we can do just that!

[tex]c=\sqrt{11^2+13^2}=17.02[/tex].

The problem asks for the answer to be rounded to the nearest tenth of a foot so, the final answer is 17 feet.