4. The window of a burning building is 24 meters above the ground.The base of a ladder is placed 10 meters from the building How long must the ladder be to reach the window? square

## Step 1<br />This problem involves the application of the Pythagorean theorem, which is a fundamental principle in geometry. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.<br /><br />## Step 2<br />In this problem, the window of the burning building is 24 meters above the ground, which represents one side of the right triangle (let's call it \(a\)). The base of the ladder is placed 10 meters from the building, which represents the other side of the right triangle (let's call it \(b\)). We are asked to find the length of the ladder, which is the hypotenuse of the right triangle (let's call it \(c\)).<br /><br />## Step 3<br />We can rearrange the Pythagorean theorem to solve for \(c\):<br />### \(c = \sqrt{a^2 + b^2}\)<br /><br />## Step 4<br />Substitute the given values into the equation:<br />### \(c = \sqrt{(24)^2 + (10)^2}\)<br /><br />## Step 5<br />Calculate the squares of 24 and 10:<br />### \(c = \sqrt{576 + 100}\)<br /><br />## Step 6<br />Add the results:<br />### \(c = \sqrt{676}\)<br /><br />## Step 7<br />Finally, take the square root of 676 to find the length of the ladder:<br />### \(c = 26\)