1. What Are Complementary and Supplementary Angles?

Complementary angles are two angles that add up to 90 degrees, while supplementary angles add up to 180 degrees. These relationships are fundamental in geometry and trigonometry.

2. How Does the Calculator Work?

The calculator uses these simple equations:

When side lengths are provided, it also calculates the hypotenuse using the Pythagorean theorem:

3. Importance of Angle Relationships

Details: Understanding complementary and supplementary angles is crucial for solving geometry problems, proving theorems, and analyzing shapes. These concepts are widely used in trigonometry, physics, and engineering.

4. Using the Calculator

Tips: Enter the known angle in degrees (0-360°). Optionally, you can enter the adjacent and opposite side lengths to calculate the hypotenuse. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Can an angle be both complementary and supplementary?
A: No, an angle cannot be both. Complementary angles sum to 90°, while supplementary angles sum to 180°.

Q2: What if my angle is greater than 90° or 180°?
A: The calculator still works, but complementary angles for angles >90° will be negative, and supplementary angles for angles >180° will be negative.

Q3: Why calculate the hypotenuse?
A: When working with right triangles, knowing all three sides helps in solving trigonometric problems and verifying angle measurements.

Q4: Can I use this for non-right triangles?
A: The hypotenuse calculation only works for right triangles. The angle relationships work for any angles.

Q5: How precise are the calculations?
A: Results are rounded to 2 decimal places, but calculations use full precision internally.