## Angles of Elevation and Depression:

You can use right triangles to findout distances, if you know an angle of elevation or an angle of depression of a object. The figure below shows each of these kinds of angles.

The angle of elevation is the angle between the horizontal line of sight and the line of sight *up* to an object. For example, if you are standing on the ground looking up at the top of a Chimeny , you could measure the angle of elevation. The angle of depression is the angle between the horizontal line of sight and the line of sight *down* to an object. For example, if you were standing on top of a hill or a building, looking down at an object, you could measure the angle of depression. You can measure these angles using a clinometer or a theodolite. People tend to use clinometers or theodolites to measure the height of trees and other tall objects. Here we will solve several problems involving these angles and

The solution depends on your height, as you measure the angle of elevation from your line of sight. Assume that you are 5 feet tall. Then the figure below shows the triangle you are solving. The figure shows us that once we find the value of |

The next example shows an angle of depression.

If we ignore the height of the person, we solve the following triangle: Given the angle of depression is 53°, angle If we take into account the height if the person, this will change the value of the adjacent side. For example, if the person is 5 feet tall, we have a different triangle: |

If you are only looking to estimate a distance, than you can ignore the height of the person taking the measurements. However, the height of the person will matter more in situations where the distances or lengths involved are smaller. For example, the height of the person will influence the result more in the tree height problem than in the building problem, as the tree is closer in height to the person than the building is.