1. What is the Angle Formula in Trigonometry?

Definition: This formula calculates an angle in a right triangle using the arctangent function based on the lengths of the opposite and adjacent sides.

Purpose: It helps determine an unknown angle when two sides of a right triangle are known, useful in geometry, physics, engineering, and navigation.

2. How Does the Angle Formula Work?

The calculator uses the formula:

Where:

• \( \theta \) — Angle in degrees
• opposite — Length of side opposite to the angle
• adjacent — Length of side adjacent to the angle

Explanation: The arctangent function (inverse tangent) converts the ratio of opposite/adjacent sides into the corresponding angle.

3. Applications of the Angle Formula

Details: Used in construction for roof pitch calculations, in navigation for bearing angles, in physics for vector analysis, and in computer graphics for rotations.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides (must be positive numbers). The calculator will return the angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for non-right triangles?
A: No, this formula specifically applies to right triangles. For other triangles, use the Law of Cosines or Law of Sines.

Q2: What units should I use for the side lengths?
A: Any consistent units (meters, feet, etc.) as long as both sides use the same units.

Q3: How accurate is the calculation?
A: The calculation is mathematically precise, though practical accuracy depends on your input measurements.

Q4: What if my angle is in radians?
A: Multiply degrees by π/180 to convert to radians, or modify the code to output radians directly.

Q5: Can I calculate the hypotenuse with this?
A: Not directly, but you could use the Pythagorean theorem: √(opposite² + adjacent²).