Question A 20 foot ladder is set against the side of a house so that it reaches up 16 feet. If Christian grabs the ladder at its base and pulls it 2 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 14 ft.) Round to the nearest tenth of a foot. Answer Attemptiout of5 ft

## 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 house is one side, and the height the ladder reaches on the house is the other side. Initially, the ladder is 20 feet long, reaches 16 feet up the house, and is 12 feet away from the house. This forms a right-angled triangle.<br /><br />## Step 3<br />When Christian pulls the ladder 2 feet farther from the house, the distance from the house becomes 14 feet. We need to find the new height the ladder reaches on the house.<br /><br />## Step 4<br />We can set up the equation using the Pythagorean theorem:<br />### \(20^2 = 14^2 + b^2\)<br /><br />## Step 5<br />Solving for \(b^2\), we get:<br />### \(b^2 = 20^2 - 14^2\)<br /><br />## Step 6<br />Taking the square root of both sides, we find the value of \(b\), which represents the new height the ladder reaches on the house.