Angle of Elevation and Angle of Depression in Trigonometry Functions

Mathematical problems that require the use of trig functions often refer to one of two special angles: the angle of elevation or the angle of depression. The scenarios that use these angles usually involve, for example, finding the distance from an airplane down to a point on the ground or the distance up to a balloon or another object above you. You can use the trig functions to solve for the missing part of a ratio or the side of an imaginary right triangle.

An angle of elevation is measured from the horizontal going upward. The horizontal is usually the ground, street, floor, or any other flat object. Even though the ground isn’t perfectly flat or horizontal, you determine the measurements with the assumption that it is. In trig, you have to consider the optimal situation — focus on the big picture, rather than on the imperfections.

The preceding figure shows an angle of elevation.

An angle of depression is measured from the horizontal going downward. In this case, the horizontal is, for example, an airplane’s flight path or a person’s line of sight while standing on a mountaintop. The angle is formed when a person on that plane or mountaintop looks at an object on the ground (or on a path parallel to the ground). Refer to the figure for a sample angle of depression.