Chapter 9 · Question 1
Define the terms (i) angle of elevation and (ii) angle of depression. What is a line of sight?
Q1
Define the terms (i) angle of elevation and (ii) angle of depression. What is a line of sight?
Answer Revealed
Direct Answer:
(i) Angle of elevation: The angle formed by the line of sight with the horizontal when the object viewed is above the horizontal level (the observer raises their head). (ii) Angle of depression: The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level (the observer lowers their head). The line of sight is the line drawn from the eye of the observer to the point in the object being viewed.
Simple Explanation
The angle of elevation is how much you look up from eye-level to see an object above you. The angle of depression is how much you look down to see an object below you.
Exam-Ready Structure
(i) Angle of elevation: When an observer looks at an object situated above the horizontal level through their eyes, the angle formed by the line of sight with the horizontal is called the angle of elevation. In other words, it is the angle between the horizontal line (at the observer's eye level) and the upward line of sight to the object. For example, looking up at the top of a tower or a flying kite. (ii) Angle of depression: When an observer looks at an object situated below the horizontal level, the angle formed by the line of sight with the horizontal is called the angle of depression. For example, looking down from a balcony at an object on the ground. Line of sight: The straight line drawn from the eye of an observer to the point on the object being viewed is called the line of sight. Key point: For a given pair of observer and object, the angle of elevation from the lower point equals the angle of depression from the higher point (alternate interior angles).
Key Points
- Angle of elevation: object above horizontal level
- Angle of depression: object below horizontal level
- Line of sight joins observer's eye to the object
- Angle of elevation = angle of depression for the same two points (alternate angles)
Common Mistakes
- Confusing angle of elevation with angle of depression
- Measuring the angle from the vertical instead of the horizontal