If you place a 26 -foot ladder against the top of a building and the bottom of the ladder is 20 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. Answer Attemptiout of 2

## Step 1<br />The problem involves the use of the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides.<br /><br />## Step 2<br />In this problem, the ladder acts as the hypotenuse, the distance from the bottom of the ladder to the building is one of the other sides, and the height of the building is the remaining side. We are given that the ladder is 26 feet long (the hypotenuse), and the distance from the bottom of the ladder to the building is 20 feet (one of the other sides). We are asked to find the height of the building (the remaining side).<br /><br />## Step 3<br />We can rearrange the Pythagorean theorem to solve for the unknown side (the height of the building):<br />### \(b = \sqrt{c^2 - a^2}\)<br /><br />## Step 4<br />Substituting the given values into the equation, we get:<br />### \(b = \sqrt{(26)^2 - (20)^2}\)<br /><br />## Step 5<br />Calculating the above expression gives us the height of the building. However, the problem asks us to round to the nearest tenth of a foot, so we round the result to 14.4 feet.