Question

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.

Answer 1

Answer: 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:

$a^2=b^2+c^2$

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:

$a^2-b^2=c^2\\\\c=\sqrt{a^2-b^2}$

In this case, you can identify that:

$a=20\ ft\\b=6\ ft\\c=x$

Then, you can substitute values into the equation $c^2=\sqrt{a^2-b^2}$ :

$x=\sqrt{(20\ ft^2)-(6\ ft)^2}$

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

Through this procedure, you get the following result:

$x=\sqrt{(20\ ft)^2-(6\ ft)^2}\\\\x=\sqrt{364\ ft^2} \\\\x\approx19.1\ ft$

Answer 2

Answer:

Step-by-step explanation:19.1 feet