1. What is the Angle Calculation?

The angle calculation using arctangent (atan) is a fundamental trigonometric operation that determines an angle in a right triangle when the lengths of the opposite and adjacent sides are known.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( \theta \) — Angle in degrees
• opposite — Length of side opposite to the angle
• adjacent — Length of side adjacent to the angle
• \( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The formula calculates the angle in radians first, then converts it to degrees by multiplying by 180/π.

3. Importance of Angle Calculation

Details: Angle calculations are essential in geometry, physics, engineering, navigation, and many practical applications involving right triangles.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in any consistent units. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of angles this can calculate?
A: The calculator can determine angles from 0° to 90° (exclusive) for positive side lengths.

Q2: What if my triangle isn't right-angled?
A: This calculator only works for right-angled triangles. For other triangles, you would need different trigonometric methods.

Q3: Why does the result need to be converted from radians?
A: The arctangent function returns values in radians by default, but degrees are often more intuitive for practical applications.

Q4: Can I use this for navigation purposes?
A: Yes, this calculation is fundamental to many navigation and surveying applications.

Q5: What about very small or very large triangles?
A: The calculator works for any size triangle as long as the proportions (opposite/adjacent) are valid.