California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

Which of the following correctly illustrates the relationship between the angle of elevation and depression?

1. Both are formed from horizontal lines extending in different directions

2. Both angles always equal 90 degrees

3. Both angles must be measured from the same point

4. Both angles can be equal in measure when viewed from the same position

The correct answer is: Both angles can be equal in measure when viewed from the same position

The correct choice illustrates that both angles of elevation and depression can be equal in measure when viewed from the same position. The angle of elevation is the angle formed when looking upward from a horizontal line, while the angle of depression is formed when looking downward from a horizontal line. When a person stands at a certain height and looks up at an object above them, the angle formed with the horizontal is the angle of elevation. Conversely, if the same person looks down to an object below them, the angle formed with the horizontal is the angle of depression. If the observer and the objects are positioned such that the line of sight to the elevated object and the line of sight to the depressed object create equal angles with the horizontal line, then these angles will indeed be the same in measurement. In practice, this can occur in various scenarios, such as when an observer stands on a hill looking at two objects that are at the same distance but at different heights. Thus, angles of elevation and depression can be equal when originating from the same viewpoint under the right circumstances.