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. In a right triangle, the two non-right angles are always complementary.

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 formula calculates the angle that, when added to the given angle θ, results in 90 degrees.

3. Importance of Complementary Angles

Details: Complementary angles are fundamental in trigonometry and geometry, especially when working with right triangles. They help in determining unknown angles and solving various geometric problems.

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: What is the range of valid input angles?
A: The input angle must be between 0° and 90°. Values outside this range don't have complementary angles in standard geometry.

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

Q3: Do complementary angles have to be adjacent?
A: No, complementary angles don't need to be adjacent. They just need to add up to 90 degrees.

Q4: How are complementary angles used in trigonometry?
A: The sine of an angle equals the cosine of its complement, and vice versa (sin(θ) = 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°.