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

Formula Used:

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

Total Surface Area of Ramp (TSA):

m²

Hypotenuse of Ramp (H):

Adjacent Side of Ramp (SAdjacent):

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 adjacent side. This formula is derived from the geometric properties of the ramp structure.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the width by considering the geometric relationships between the ramp's surface area and its dimensional components.

3. Importance of Width Calculation

Details: Accurate width calculation is crucial for ramp design, construction planning, and ensuring proper dimensions for accessibility and safety standards.

4. Using the Calculator

Tips: Enter total surface area in m², hypotenuse in meters, and adjacent side in meters. All values must be positive, and the hypotenuse must be greater than the adjacent side.

5. Frequently Asked Questions (FAQ)

Q1: What units should be used for input values?
A: All input values should be in consistent units (meters for length, square meters for area).

Q2: Why must the hypotenuse be greater than the adjacent side?
A: This is a geometric requirement from the Pythagorean theorem for a valid right triangle.

Q3: Can this formula be used for any ramp shape?
A: This formula is specifically designed for rectangular ramps with a right triangular cross-section.

Q4: What if I get a negative result?
A: A negative result indicates invalid input values that don't form a valid geometric configuration.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the given geometric model, assuming precise input measurements.