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 when given one angle (θ).

2. How Does the Calculator Work?

The calculator uses the complementary angle formula:

Where:

• \( \theta \) — Given angle in degrees (must be between 0° and 90°)
• 90° — Right angle measure

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between complementary and supplementary angles?
A: Complementary angles add up to 90°, while supplementary angles add up to 180°.

Q2: Can an angle have more than one complementary angle?
A: No, each angle has exactly one complementary angle (unless you consider negative angles or angles beyond 360°).

Q3: What is the complement of 0°?
A: 90° is the complement of 0°.

Q4: Are the angles in a right triangle complementary?
A: Yes, the two non-right angles in a right triangle are always complementary.

Q5: How are complementary angles used in trigonometry?
A: Trigonometric functions of complementary angles are related (e.g., sin(θ) = cos(90°-θ)).