1. What is a Complementary Angle?

Complementary angles are two angles whose measures add up to 90 degrees. When two angles are complementary, each angle is said to be the complement of the other. This concept is fundamental in geometry and trigonometry.

2. How Does the Calculator Work?

The calculator uses the complementary angle formula:

Where:

• \( \theta \) — Given angle in degrees
• \( 90^\circ \) — Right angle measurement

Explanation: The formula calculates the angle that, when added to the given angle θ, results in a sum of 90 degrees.

3. Importance of Complementary Angles

Details: Complementary angles are essential in various mathematical applications, including trigonometry, geometry proofs, and real-world applications such as construction, engineering, and navigation where right angles are involved.

4. Using the Calculator

Tips: Enter the angle θ in degrees (must be between 0 and 90 degrees). The calculator will compute the complementary angle that, when added to θ, equals 90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid input angles?
A: The input angle θ must be between 0 and 90 degrees inclusive. Angles outside this range cannot have a complementary angle within the standard definition.

Q2: Can complementary angles be negative?
A: No, complementary angles are always positive angles that sum to 90 degrees. Negative angles are not considered in this context.

Q3: What's the difference between complementary and supplementary angles?
A: Complementary angles sum to 90 degrees, while supplementary angles sum to 180 degrees.

Q4: Are complementary angles always adjacent?
A: No, complementary angles don't have to be adjacent. They only need to sum to 90 degrees, regardless of their position.

Q5: Can two obtuse angles be complementary?
A: No, since obtuse angles are greater than 90 degrees, two obtuse angles would sum to more than 180 degrees, making it impossible for them to be complementary.