- 1. Horizontal and Vertical: The Two Lines Everything Rests On
Identify horizontal and vertical lines and planes in real situations and recognise that a vertical line meets a horizontal line at a right angle.
- 2. Looking Up: The Line of Sight and the Angle of Elevation
Define the line of sight and the angle of elevation as the angle between the horizontal and an upward line of sight, and identify it correctly at the observer in diagrams and word problems.
- 3. Looking Down: The Angle of Depression
Define the angle of depression as the angle between the horizontal and a downward line of sight, draw the horizontal at the observer's eye, and tell depression apart from elevation.
- 4. Elevation Equals Depression: The Relationship
State and prove that the angle of elevation from a low point equals the angle of depression from the high point (alternate angles between parallel horizontals), and use it to find missing angles.
- 5. Finding the Answer by Accurate Drawing
Turn an elevation or depression word problem into an accurate scale drawing of a right-angled triangle, choose a sensible scale, and measure an unknown length or angle from the drawing.
- 6. Real-World Problems: Elevation and Depression Together
Decide whether a mixed real-world scene is elevation or depression, solve it by accurate drawing (including depression and non-45-degree cases), and combine the equal-angles relationship with drawing in two-part problems.
