1. What is the Complementary Angle Theorem?

The Complementary Angle Theorem states that two angles are complementary if their measures add up to 90 degrees. This calculator finds the complementary angle for any given angle between 0 and 90 degrees.

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 calculator simply subtracts your input 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 non-right angles are always complementary. They're also important in trigonometry and various engineering applications.

4. Using the Calculator

Tips: Enter any angle between 0 and 90 degrees. The calculator will return its complement (the angle that when added to your input equals 90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What if I enter an angle greater than 90 degrees?
A: The calculator will only accept values between 0 and 90 degrees, as angles beyond this range don't have complements in standard geometry.

Q2: Can complementary angles be negative?
A: No, angle measures in standard geometry are always positive values between 0° and 90° for complementary angles.

Q3: Are complementary angles always adjacent?
A: No, complementary angles don't need to be adjacent - they just need to add up to 90 degrees regardless of their position.

Q4: What's the difference between complementary and supplementary angles?
A: Complementary angles sum to 90 degrees, while supplementary angles sum to 180 degrees.

Q5: How are complementary angles used in trigonometry?
A: In right triangles, the sine of one angle equals the cosine of its complement (hence "co-sine").