1. What is Slope in a Right Triangle?

The slope of a right triangle is the ratio of the vertical change (rise) to the horizontal change (run) of the hypotenuse. It's mathematically equal to the tangent of the angle between the hypotenuse and the horizontal side.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( \theta \) — Angle between hypotenuse and horizontal side (degrees)
• \( \tan \) — Trigonometric tangent function

Explanation: The tangent of an angle in a right triangle represents the ratio of the opposite side to the adjacent side, which is exactly the slope.

3. Importance of Slope Calculation

Details: Slope calculations are essential in various fields including engineering, construction, physics, and navigation. They help determine steepness, design ramps, analyze terrain, and more.

4. Using the Calculator

Tips: Enter the angle in degrees (must be between 0 and 90 degrees). The calculator will compute the slope as a dimensionless ratio.

5. Frequently Asked Questions (FAQ)

Q1: What does a slope of 1 mean?
A: A slope of 1 means a 45° angle, where the rise equals the run (vertical and horizontal changes are equal).

Q2: How is slope different from angle?
A: Slope is a ratio (rise/run) while angle is measured in degrees. They are mathematically related through the tangent function.

Q3: What's the maximum possible slope value?
A: As the angle approaches 90°, the slope approaches infinity. At exactly 90°, the slope is undefined.

Q4: Can slope be negative?
A: In this right triangle context, slope is always positive (0° to 90°). Negative slopes occur when dealing with downward inclines beyond this context.

Q5: How is slope used in real-world applications?
A: Slope is used in road design (gradients), roof pitch calculations, wheelchair ramp design, and many engineering applications.