The angle of elevation is the angle between the horizontal plane and an observer and an object. It can be measured using devices like sextants and can be used to determine the height and distance of an object. Trigonometry can be used to solve for unknown values.
The angle of elevation is the measure of the angle formed by the horizontal plane at which an observer and an object are located above the horizontal plane. The observer is at the apex of the angle. The intersection of the angle radii with the vertical line from the object to the horizontal plane forms a right triangle. There are several ways to determine this angle, given a known height and distance, and devices such as sextants can be used to measure the angle. Given a known elevation angle, the height and distance of the observed object can be determined.
If the observer is directly below the object whose elevation angle is being measured, the angle is 90 degrees. An object in the same horizontal plane as the observer has an elevation of zero degrees. The elevation angle measurement can fall anywhere between these two values.
Although the sextant is the instrument traditionally used to measure the elevation angle of celestial objects for navigational purposes, it can be used to determine the elevation angle of any object. To use a sextant, the observer holds the instrument over one eye and points it at the elevated object. The degree marks on the sextant indicate the angle formed by the horizontal plane of the observer and the intersecting ray pointing towards the elevated object.
The geometric and mathematical concepts associated with right triangles can be used to determine unknown values of distance and angle, and simple trigonometry can be used to solve for unknown values as long as at least two are known. If the height of the object and the distance to the observer are known, the angle of elevation can be determined by finding the tangent of the angle, the ratio of height to distance. If the angle and height or distance are known, the unknown can be determined in the same way. It is also possible to determine the elevation angle when only one known value is given, although this requires the use of more advanced trigonometric concepts.
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