Brian borrowed a 20 foot extension ladder to use when he paints his house. if he sets the base of the ladder 6 feet from the house, as shown below, how far up will the top of the ladder reach? round to one decimal place.

19.1 feet.

Step-by-step explanation:

Draw a right triangle as the one shown attached, where "x"  is the height in feet that the top of the ladder will reach.

You need to use the Pythagorean Theorem:

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

If you solve for one of the legs, you get:

In this case, you can identify that:

Then, you can substitute values into the equation :

Finally, you must evaluate in  order to find the value of "x".

Through this procedure, you get the following result:

.

step-by-step explanation:

x = 3 ± √(5+y)