We are given a ladder that is 16 meters long is placed against a wall. We have the following diagram:
To determine the value of the height "h" we can use the Pythagorean theorem since the ladder and the wall form a right triangle.

Solving the squares:

Now, we subtract 16 from both sides:

Now, we take the square root to both sides:

Therefore, the height is 15.5 meters.