A loading dock at a warehouse in Alexandria has a ramp that is 16 feet in length. The length from the edge of the loading dock to the end of the ramp is 14 feet. Which is the closest to the height of the loading dock?

To find the height of the loading dock, we can use the Pythagorean theorem. The ramp, the height of the loading dock, and the distance from the edge of the loading dock to the end of the ramp form a right triangle.

Let $h$ be the height of the loading dock. According to the Pythagorean theorem:

$$h^2 + 14^2 = 16^2$$

Calculating the squares:

$$h^2 + 196 = 256$$

Now, subtract 196 from both sides:

$$h^2 = 256 - 196$$ $$h^2 = 60$$

Taking the square root of both sides:

$$h = \sqrt{60} \approx 7.75$$

Thus, the height of the loading dock is approximately 7.75 feet.