1. Triangle Angle Calculation Methods

There are two primary methods to calculate an unknown angle in a triangle: using trigonometric functions in right triangles, or using the sum of angles property for any triangle.

2. Right Triangle Angle Calculation

For right triangles, you can use trigonometric functions:

Where:

• \( \theta \) — The unknown angle in degrees
• opposite — Length of the side opposite to the angle
• hypotenuse — Length of the hypotenuse

Note: This method only works for right triangles where one angle is exactly 90°.

3. Sum of Angles Calculation

For any triangle, the sum of interior angles is always 180°:

Where:

• \( \theta \) — The unknown angle in degrees
• angle₁ — First known angle
• angle₂ — Second known angle

4. Using the Calculator

For right triangles: Enter the lengths of the opposite side and hypotenuse.
For sum of angles: Enter the two known angles.
The calculator will automatically determine the unknown angle.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for non-right triangles?
A: Only the sum of angles method works for all triangles. The trigonometric method is only for right triangles.

Q2: What if I know all three sides but no angles?
A: You can use the Law of Cosines first to find an angle, then use this calculator.

Q3: Why does my right triangle calculation give an error?
A: The opposite side must be ≤ hypotenuse in a right triangle. Check your measurements.

Q4: Can angles be negative?
A: No, angles in a triangle must be between 0° and 180°.

Q5: How precise are the results?
A: Results are rounded to one decimal place. For exact values, use exact fractions or symbolic computation.