1. What is the Distance from Height and Angle Formula?

The distance formula calculates the horizontal distance (D) from a known height (H) and angle of elevation (θ). This trigonometric relationship is commonly used in surveying, navigation, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( D \) — Horizontal distance (units)
• \( H \) — Height or vertical measurement (units)
• \( \theta \) — Angle of elevation (degrees)

Explanation: The tangent of the angle equals the ratio of opposite side (height) to adjacent side (distance), allowing us to solve for distance when height and angle are known.

3. Importance of Distance Calculation

Details: Accurate distance calculation from height and angle is essential in fields like architecture, construction, military targeting, and geographic surveying where direct measurement may be impractical.

4. Using the Calculator

Tips: Enter height in consistent units, angle in degrees (must be between 0 and 90). The calculator will compute the horizontal distance in the same units as the height.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Any consistent units can be used (meters, feet, etc.) as long as height and distance use the same units.

Q2: What angle range is valid?
A: Angles must be between 0 and 90 degrees (exclusive). At exactly 90°, the tangent is undefined.

Q3: Can this be used for angles of depression?
A: Yes, the same formula applies when measuring downward angles from a height.

Q4: How accurate is this method?
A: Accuracy depends on precise measurement of both height and angle. Small angle measurement errors significantly affect results at long distances.

Q5: What about atmospheric refraction?
A: For very long distances (especially in surveying), atmospheric refraction may need to be accounted for in precise calculations.