One type of angle that occurs in many applications is the angle of elevation of a given point with respect to a point that is at a lower elevation and at some positive horizontal distance from it.

Another important angle is the angle of depression of a given point with respect to a point that is at a higher elevation and at some positive horizontal distance from it. In this sub-topic, we will see how trigonometry is used for finding the heights and distances of various objects without actually measuring them. For example, the height of a tower, mountain, building or tree, distance of a ship from a light house, width of a river, etc. can be determined by using knowledge of trigonometry.

The process of finding heights and distances is the best example of applying trigonometry in real-life situations. We would explain these applications through some examples. Before studying methods to find heights and distances, we should understand some basic definitions.

Definition
The line which is drawn from the eyes of the observer to the point being viewed on the object is known as the line of sight.

The line PQ represents the line of sight, some times it can be called as line vision.

Definition
The angle of elevation of the point on the object (above the horizontal line) viewed by the observer is the angle which is formed by the line of sight with the horizontal line.

The angle of elevation of Q with respect to P is θ and the angle of depression of P with respect to Q is α.

Note
The angle of elevation and the angle of depression are acute angles and are defined to have positive measure.

Using the concepts of angle of elevation and depression, let us solve some examples related to the problem of height and distance.