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 θ between 0 and 90 degrees.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( θ \) — The given angle in degrees (must be between 0° and 90°)
• 90° — The sum of two complementary angles

Explanation: For any angle θ, its complementary angle is what needs to be added to it to make 90 degrees.

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 the known angle θ in degrees (must be between 0 and 90). The calculator will compute its complementary angle.

5. Frequently Asked Questions (FAQ)

Q1: Can an angle have more than one complementary angle?
A: No, each angle θ has exactly one complementary angle (90° - θ).

Q2: What if my angle is greater than 90 degrees?
A: Angles greater than 90° don't have complementary angles in standard geometry (they would have supplementary angles instead).

Q3: Are the angles in a right triangle complementary?
A: Yes, the two non-right angles in a right triangle are always complementary.

Q4: 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)).

Q5: What's the difference between complementary and supplementary angles?
A: Complementary angles sum to 90°, while supplementary angles sum to 180°.