Construct the diagram by translating each statement into a geometric feature, then label given lengths, angles, directions, and unknowns. For IB Mathematics AA SL 3.3, the diagram must represent bearings, elevation, or depression before trigonometry is applied.
The IB command term construct means “display information in a diagrammatic or logical form.” Use this method before calculating anything:
| Step | What to do |
|---|---|
| 1. Identify objects | Represent objects or locations as points, such as , , and . |
| 2. Draw references | Add ground, horizontal, vertical, or north lines as required. |
| 3. Connect points | Use segments for paths and a line of sight for viewing directions. |
| 4. Label givens | Put each known length or angle beside its segment or vertex. |
| 5. Mark the unknown | Use a variable such as ; do not calculate it yet. |
| 6. Check | Confirm every relationship and reference line matches the wording. |
For example, suppose a person stands from a tower and observes its top at an angle of elevation of . Draw a horizontal ground segment of , a vertical tower, and a line of sight to the top. Place between the horizontal and line of sight, and label the tower height .
For a bearing, draw a north line at the starting point and measure the angle clockwise from north. Bearings use three figures, such as . An angle of depression is measured downward from a horizontal line at the observer, not from the vertical.
A common misconception is that the angle of elevation belongs at the top of the object. It belongs at the observer between the horizontal and line of sight.
Exam technique: This skill applies to AA SL Papers 1 and 2. Examiners expect a clearly labelled diagram supporting the correct trigonometric setup. An incorrect reference angle usually produces an incorrect method.