The angle between a ramp's height and base equals 90 degrees. The two lengths and the length of the ramp therefore form a right triangle, and the dimensions follow the same trigonometric relationship as all right triangles. The square of the ramp's height is the difference between the squares of the ramp's length and its base's length. The formula relating these three lengths is the Pythagorean theorem.

Square the length of the ramp's base. If it measures, for instance, 10 feet, then 10^2 = 100.

Square the ramp's diagonal. If it measures, for instance, 13 feet in length, then 13^2 = 169.

Subtract the smaller square from the larger one  169  100 = 69.

Find the square root of the answer  69^0.5 = 8.3 feet. This is the ramp's height.
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