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Distance Formula:
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The distance formula calculates the horizontal distance (D) from an object when you know its height (H) and the angle of elevation (θ). This is based on trigonometric principles and is commonly used in surveying, navigation, and various engineering applications.
The calculator uses the distance formula:
Where:
Explanation: The tangent of the angle equals the ratio of opposite side (height) to adjacent side (distance), so we rearrange to solve for distance.
Details: This calculation is used in surveying to measure distances to inaccessible points, in architecture for site planning, in military for range finding, and in various scientific measurements where direct distance measurement isn't possible.
Tips: Enter height in consistent units (meters, feet, etc.), and angle in degrees (must be between 0 and 90 degrees). The calculator will return distance in the same units as the height input.
Q1: What if my angle is greater than 90 degrees?
A: This formula only works for angles between 0 and 90 degrees. For angles approaching 90°, the distance approaches zero (directly overhead).
Q2: How accurate is this calculation?
A: Accuracy depends on precise measurement of both height and angle. Small angle measurement errors can lead to significant distance errors at long ranges.
Q3: Does this account for Earth's curvature?
A: No, for distances over about 1km or heights over 100m, Earth's curvature becomes significant and this simple formula becomes less accurate.
Q4: Can I use this for downward angles?
A: Yes, the same formula works for angles of depression (looking downward), just use the vertical distance to the object as height.
Q5: 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.