1. What is a Complementary Angle?

Two angles are complementary when their measures add up to 90 degrees. If one angle is known, its complement can be found by subtracting it from 90°.

2. How Does the Calculator Work?

The calculator uses the complementary angle formula:

Where:

• \( \theta \) — Given angle in degrees
• 90° — Right angle measure

Explanation: The formula simply subtracts the given angle from 90 degrees to find its complement.

3. Importance of Complementary Angles

Details: Complementary angles are fundamental in geometry, especially in right triangles where the two non-right angles are always complementary. They're also important in trigonometry and various engineering applications.

4. Using the Calculator

Tips: Enter an angle between 0 and 90 degrees. The calculator will compute its complement (the angle that when added to it makes 90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Can an angle be complementary to itself?
A: Yes, a 45° angle is complementary to itself since 45° + 45° = 90°.

Q2: What's the difference between complementary and supplementary angles?
A: Complementary angles add to 90°, while supplementary angles add to 180°.

Q3: Can more than two angles be complementary?
A: No, by definition only two angles can be complementary as their sum must be exactly 90°.

Q4: Do complementary angles have to be adjacent?
A: No, they don't need to be adjacent. They just need to add up to 90°.

Q5: How are complementary angles used in trigonometry?
A: The sine of an angle equals the cosine of its complement, and vice versa (sinθ = cos(90°-θ)).