This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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: \[ h = sqrt(60) ≈ 7.75 \] Thus, the height of the loading dock is approximately 7.75 feet.