Answer:
hypotenuse = x √(1 + s²)
Explanation:
The slope of a ramp (s) is the ratio of the height (y) to the width (x). For a right triangle, Pythagorean's theorem says that the square of the hypotenuse is equal to the width squared plus the height squared. Using these two equations, we can find the hypotenuse in terms of the width.
First, use the slope to find the height in terms of the width.
s = y / x
y = sx
Next, use Pythagorean's theorem to find the hypotenuse in terms of the width.
(hypotenuse)² = x² + y²
(hypotenuse)² = x² + (sx)²
(hypotenuse)² = x² + s²x²
(hypotenuse)² = x² (1 + s²)
hypotenuse = x √(1 + s²)
