1. What is Tan Ratio?

The tangent (tan) of an angle in a right triangle is the ratio of the length of the opposite side (rise) to the length of the adjacent side (run). It's a fundamental trigonometric function used in mathematics, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the tan ratio formula:

Where:

• \( \tan(\theta) \) — Tangent of angle θ (dimensionless)
• \( \text{rise} \) — Length of opposite side (meters)
• \( \text{run} \) — Length of adjacent side (meters)

Explanation: The ratio represents how steep a line or surface is relative to horizontal.

3. Importance of Tan Ratio

Details: The tan ratio is essential for calculating slopes, angles of elevation/depression, and in various engineering applications like road design, roof pitch, and mechanical systems.

4. Using the Calculator

Tips: Enter rise and run values in meters (must both be positive numbers). The calculator will compute the dimensionless tan ratio.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between tan and slope?
A: Tan ratio gives the tangent of the angle (opposite/adjacent), while slope is rise over run. They're numerically equal for small angles.

Q2: What are typical tan ratio values?
A: Common values range from 0 (horizontal) to ∞ (vertical), with 1 representing a 45° angle.

Q3: How is tan ratio used in real life?
A: Used in construction (ramps, roofs), road design (gradients), and physics (force components).

Q4: What are the limitations of this calculation?
A: Only valid for right triangles. For other cases, more complex trigonometry is needed.

Q5: Can I calculate the angle from the tan ratio?
A: Yes, using the arctangent (tan⁻¹) function: θ = tan⁻¹(opposite/adjacent).