1. What is Zenith Angle and Vertical Angle?

The zenith angle is the angle between the zenith (directly overhead) and a line of sight to a point. The vertical angle (also called elevation angle) is the angle between the horizon and the point. They are complementary angles that sum to 90 degrees.

2. How Does the Calculator Work?

The calculator uses the simple complementary angle formula:

Where:

• \( \text{Zenith Angle} \) — Angle from zenith (0-90 degrees)
• \( \text{Vertical Angle} \) — Angle from horizon (0-90 degrees)

Explanation: Since the zenith angle and vertical angle are complementary, their sum always equals 90 degrees.

3. Importance of Angle Conversion

Details: Converting between zenith and vertical angles is essential in astronomy, surveying, navigation, and satellite communication where different systems use different angle references.

4. Using the Calculator

Tips: Enter the zenith angle in degrees (0-90). The calculator will compute the corresponding vertical angle. Both angles are measured in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid zenith angles?
A: Zenith angles range from 0° (directly overhead) to 90° (at the horizon).

Q2: What is the corresponding vertical angle range?
A: Vertical angles range from 90° (directly overhead) to 0° (at the horizon).

Q3: Can zenith angle be greater than 90 degrees?
A: No, by definition, zenith angle is measured from the zenith (0°) to the horizon (90°).

Q4: Where is this conversion commonly used?
A: Astronomy (telescope positioning), surveying (theodolite measurements), and satellite tracking systems.

Q5: Are there any special cases to consider?
A: For angles below the horizon (negative vertical angles), different conventions apply and this simple conversion doesn't work.