Width of Ramp given Total Surface Area, Opposite Side and Hypotenuse Calculator

Width of Ramp Formula:

\[ w = \frac{TSA - (\sqrt{H^2 - SOpposite^2} \times SOpposite)}{\sqrt{H^2 - SOpposite^2} + SOpposite + H} \]

Total Surface Area of Ramp (TSA):

m²

Hypotenuse of Ramp (H):

Opposite Side of Ramp (SOpposite):

Width of Ramp (w):

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1. What is the Width of Ramp Formula?

The Width of Ramp formula calculates the width of a ramp given its total surface area, hypotenuse, and opposite side. This formula is derived from the geometric properties of a right triangle formed when a rectangular plane is raised at an angle to create a ramp.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ w = \frac{TSA - (\sqrt{H^2 - SOpposite^2} \times SOpposite)}{\sqrt{H^2 - SOpposite^2} + SOpposite + H} \]

Where:

\( w \) — Width of Ramp (m)
\( TSA \) — Total Surface Area of Ramp (m²)
\( H \) — Hypotenuse of Ramp (m)
\( SOpposite \) — Opposite Side of Ramp (m)

Explanation: The formula calculates the width by first determining the adjacent side using the Pythagorean theorem, then solving for width using the total surface area and the perimeter components.

3. Importance of Width Calculation

Details: Calculating the width of a ramp is essential for construction, accessibility planning, and ensuring compliance with building codes and regulations for ramp dimensions.

4. Using the Calculator

Tips: Enter total surface area in square meters, hypotenuse and opposite side in meters. All values must be positive, and the hypotenuse must be greater than the opposite side.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: Use consistent units, preferably meters for length measurements and square meters for area measurements.

Q2: Why must the hypotenuse be greater than the opposite side?
A: This is a requirement of the Pythagorean theorem - the hypotenuse must always be the longest side in a right triangle.

Q3: Can this formula be used for any type of ramp?
A: This formula specifically applies to ramps formed by raising a rectangular plane at an angle, creating a right triangular prism.

Q4: What if I get a negative result for width?
A: A negative result typically indicates invalid input values that don't correspond to a physically possible ramp configuration.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for the given inputs, assuming the ramp follows the described geometric model.