6. Two vertical posts stand side by side. One post is 8 feet tall and the other is 17 feet tall.If a 24-foot wire is stretched between the tops of the posts, how far apart are the posts?

## Step 1<br />This 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 /><br />## Step 2<br />In this problem, the two posts form a right-angled triangle with the wire as the hypotenuse. The height of the posts are the two sides of the triangle, and the distance between the posts is the base of the triangle.<br /><br />## Step 3<br />We know the height of the posts (a and b) are 8 feet and 17 feet, and the wire (c) is 24 feet. We need to find the base (b), which is the distance between the posts.<br /><br />## Step 4<br />We can rearrange the Pythagorean theorem to solve for b:<br />### \(b = \sqrt{c^2 - a^2}\)<br /><br />## Step 5<br />Substitute the given values into the equation:<br />### \(b = \sqrt{(24)^2 - (8)^2}\)<br /><br />## Step 6<br />Calculate the square of 24 and 8, subtract the latter from the former, and then take the square root of the result.