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

Which of the following is true about the angle of depression?

1. It can only exist in a straight line

2. It is measured directly downward

3. It is the same as the angle of elevation when viewed from a position below

4. It measures how far a point is from the observer

The correct answer is: It is the same as the angle of elevation when viewed from a position below

The angle of depression is defined as the angle formed between a horizontal line from the observer's eye and the line of sight down to an object below the horizontal level. When you consider the angle of elevation, which is measured from the horizontal line up to an object above the observer's eye level, you can see the relationship between the two angles. In scenarios where an observer is at a lower position looking up at an object, the angle of elevation from that position to the object is equal to the angle of depression when viewed from a higher position looking down at the same object. This relationship holds true because both angles are formed relative to the same horizontal line and arise from the same two points of reference, thereby establishing their equality. Consequently, recognizing this relationship aids in various practical applications in fields such as navigation, architecture, and physics. The other options do not accurately reflect the properties of the angle of depression. The angle cannot only exist in a straight line, as it involves a vertical change; it is not measured directly downward, but rather from horizontal down to the object; and it does not measure the distance from the observer to the point, but rather the angle related to the observer's horizontal line of sight.