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How to Calculate Elevation Degrees From Ground to Air for Range & Altitude

The idle investigations of mathematicians sometimes turn out to be anything but idle. More than 2,000 years ago, Pythagorus, for example, discovered a property that related the three sides of a right triangle. Since then, applications of the special properties of right triangles have gone far beyond the esoteric and philosophical right into the practical, such as calculating elevation angle from range and altitude.

Instructions

- 1
  Draw a right triangle that represents the situation. Start with a horizontal line with your location on one end and the other end immediately underneath the target object. The vertical leg goes from the ground to the height of the object and the hypotenuse is the straight line connecting the object to your location.
- 2
  Write in the distances corresponding to the situation. The vertical leg will be the altitude. The range can be given in two ways -- ground range is the distance along the ground to the spot underneath the target, and slant range is the distance through the air directly from the observer to the target. Ground range would be marked on the horizontal leg of the triangle, slant range would be marked on the hypotenuse. For example, you could be given an object at 300 yards in height with a ground range of 1,800 yards, or a height of 300 yards and a slant range of 1,775 yards.
- 3
  Calculate the inverse trigonometric function corresponding to the information you have. The elevation angle is equal to the inverse sine (or arcsin) of the height/(ground range), or it is equal to the inverse tangent (arctan) of the height/(slant range). Choose the formula that uses the information you have. For the example that gives the ground range, the angle would be arcsin(300/1800) = 9.6 degrees of elevation. If you were given the slant range instead, the angle would be arctan(300/1775) = 9.6 degrees.

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