To find the horizontal distance \( x \) from the camera to Michael, we can use the information given and apply the Pythagorean theorem.
We have:
- The height of the camera above Michael: \( 25 \) ft.
- The slant height (the hypotenuse of the right triangle): \( 39 \) ft.
First, we calculate the total height from the ground to the camera: \[ \text{Total height of the camera} = \text{Height of Michael} + \text{Height of camera above Michael} = 5, \text{ft} + 25, \text{ft} = 30, \text{ft}. \]
Now, we can create a right triangle where:
- The vertical side (height difference) is \( 25, \text{ft} \),
- The hypotenuse (slant height) is \( 39, \text{ft} \),
- The horizontal distance from the camera to Michael is \( x \).
Using the Pythagorean theorem: \[ \text{Hypotenuse}^2 = \text{Vertical side}^2 + \text{Horizontal side}^2, \] we substitute the known values: \[ 39^2 = 25^2 + x^2. \]
Calculating the squares: \[ 1521 = 625 + x^2. \]
Now, solve for \( x^2 \): \[ x^2 = 1521 - 625 = 896. \]
Then, take the square root of both sides to find \( x \): \[ x = \sqrt{896} \approx 29.98. \]
Rounding to two decimal places gives us \( x \approx 29.91 \).
Thus, the horizontal distance \( x \) of the camera is approximately 29.91 ft.