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The angle of elevation distance calculation determines how far an object is from an observer based on its height and the angle at which it's viewed. This is a fundamental trigonometric calculation used in surveying, navigation, and various engineering applications.
The calculator uses the trigonometric formula:
Where:
Explanation: The tangent of the angle equals the ratio of the opposite side (height) to the adjacent side (distance), allowing us to solve for distance when height and angle are known.
Details: Accurate distance calculation using angle of elevation is crucial in fields like architecture, astronomy, aviation, and military targeting. It allows for non-contact measurement of distances to inaccessible objects.
Tips: Enter height in meters and angle in radians (0 to π/2). For degrees, convert to radians first (radians = degrees × π/180). Both values must be positive numbers.
Q1: Why use radians instead of degrees?
A: Radians are the standard angular measurement in mathematics. Most programming languages' trigonometric functions use radians.
Q2: What's the maximum valid angle?
A: The angle must be less than 90° (π/2 radians). At exactly 90°, the tangent is undefined as the object would be directly overhead.
Q3: How accurate is this calculation?
A: It's mathematically precise for ideal conditions. In practice, factors like atmospheric refraction and measurement errors affect real-world accuracy.
Q4: Can I use this for downward angles?
A: For angles of depression (looking downward), the same formula applies if you consider the height as the vertical drop.
Q5: What if I only know the angle in degrees?
A: Convert degrees to radians by multiplying by π/180 (≈0.0174533). For example, 45° = 45 × π/180 ≈ 0.7854 radians.