Lecture Notes: Introduction to Angles of Elevation and Depression
Summary
Today's class explored the concept of angles of elevation and depression, which occur when one looks up or down from a horizontal line of sight to an object. We've used various everyday scenarios involving a character named Dylan at a park to observe and understand these angles in real-world settings.
Key Concepts
Definitions
- Angle of Elevation: The angle formed between the horizontal line of sight and the line from the observer to an object above the observer.
- Angle of Depression: The angle formed between the horizontal line of sight and the line from the observer to an object below the observer.
Observations with Dylan
- Bird on a tree: As Dylan looks up to see the bird, the angle formed is an angle of elevation. This angle gives the bird a higher position relative to Dylan's straight-ahead (horizontal) view.
- Signboard direction: When Dylan looks up towards a signboard for directions, he notes the angle of elevation which increases as he moves closer to the signboard.
- Crocodile farm encounter: As Dylan looks down at a crocodile, the angle his sight makes below the horizontal is an angle of depression.
- Mudskipper sighting: Dylan observes a mudskipper and the angle of depression increases because the mudskipper is closer compared to the crocodile, making the angle larger.
Components of Angles in Elevation and Depression
- Horizontal Line: A straight line that we regard as the baseline or the line from the observer’s eye when looking straight ahead.
- Line of Sight: The line along which an observer has unobstructed vision from his eye to the object of focus.
- Both angles involve these two lines, where the angle of elevation or depression is the angle formed between these lines at the observer's position.
Interesting Findings
- Relation between Angles of Elevation and Depression: In a scenario where Dylan and a squirrel are looking at each other, respectively from above and below, the angle of elevation (from Dylan to the squirrel) and the angle of depression (from the squirrel to Dylan) are equal because of the parallel nature of their horizontal lines and the line of sight being the same.
Conclusion
The angles of elevation and depression are fundamentally similar as both involve the horizontal line and the line of sight from an observer's perspective. Understanding these angles aids in better comprehending various visual and practical scenarios in everyday life.