Angles of Elevation, Depression and Bearings
Learn angles of elevation, depression and bearings for IB MYP Extended Maths Year 5. Apply right-angle trig to real-world navigation and surveying contexts.
What This Topic Covers
This topic applies right-angle trigonometry to two specific real-world contexts: angles of elevation and depression, and compass bearings. Both appear regularly in MYP Extended assessments and require you to construct an appropriate triangle from a written or visual description.
Angles of Elevation and Depression
An angle of elevation is measured upward from the horizontal to a point above the observer. An angle of depression is measured downward from the horizontal to a point below the observer. In both cases, the horizontal line and the line of sight form a right-angled triangle with a vertical height.
Key Step
Draw the horizontal line at the observer's eye level. The angle of elevation or depression is always measured from this horizontal — not from the vertical or the slope.
Bearing Problems
Bearings are measured clockwise from North, expressed as three-figure numbers (e.g. 045°, 270°). In MYP trig problems, bearings are used to set up a triangle between two or more points, and you then use sin, cos, or tan to find a distance or direction.
- Identify North at the starting point first.
- Mark the bearing angle clockwise from North.
- Identify the right angle in the resulting triangle (often the vertical or horizontal component).
Common Mistakes
- Confusing elevation (looking up) with depression (looking down) when labelling the diagram
- Measuring the bearing from South or from the line of travel rather than from North
- Forgetting alternate angles when North lines are parallel — a common geometry step in bearing diagrams
MYP Criterion D Connection
These problems are a favourite for Criterion D tasks because they link mathematics to realistic navigation and surveying contexts. You will be expected to interpret your calculated angle or distance within the scenario described.