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 1This 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:### where is the length of the hypotenuse, and and are the lengths of the other two sides.## Step 2In 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 ). 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 ). We are asked to find the length of the ladder, which is the hypotenuse of the right triangle (let's call it ).## Step 3We can rearrange the Pythagorean theorem to solve for :### ## Step 4Substitute the given values into the equation:### \(c = \sqrt{(24)^2 + (10)^2}\)## Step 5Calculate the squares of 24 and 10:### ## Step 6Add the results:### ## Step 7Finally, take the square root of 676 to find the length of the ladder:###