1. What is the Angle Ratio Formula?

The angle ratio formula calculates an angle in a right triangle using the inverse tangent (arctangent) function. Given the lengths of the opposite and adjacent sides, it determines the angle between the adjacent side and the hypotenuse.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( \theta \) — The angle in degrees
• \( O \) — Length of the opposite side
• \( A \) — Length of the adjacent side
• \( \tan^{-1} \) — Inverse tangent function (arctangent)

Explanation: The formula calculates the ratio of the opposite side to the adjacent side, then finds the angle whose tangent equals that ratio.

3. Importance of Angle Calculation

Details: Calculating angles from side ratios is fundamental in trigonometry, with applications in navigation, engineering, physics, computer graphics, and construction.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in any consistent units. Both values must be positive numbers. The calculator will return the angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What if the adjacent side is zero?
A: The adjacent side cannot be zero as division by zero is undefined. This would represent a vertical line with an angle of 90 degrees.

Q2: How accurate is this calculation?
A: The calculation is mathematically precise for the given inputs. The accuracy depends on the precision of your side measurements.

Q3: Can I use this for non-right triangles?
A: No, this formula specifically applies to right triangles. For other triangles, you would need to use the Law of Sines or Law of Cosines.

Q4: What's the difference between arctan and inverse tan?
A: They are the same function. Both terms refer to the inverse of the tangent function.

Q5: How do I convert the result to radians?
A: Multiply the degree value by π/180. Most programming languages and calculators have built-in functions for this conversion.