① Angles of elevation and depressionCalculator useful
Both angles are measured from the horizontal. The picture only sets the scene: draw your own right-angled triangle from it, then use SOH CAH TOA. The angle of depression from the top is equal to the angle of elevation looking back up.
② Three-figure bearings and back bearingsCalculator useful
A bearing is measured clockwise from north and always has three figures (so 7° is written 007°). Check which line the marked angle is measured from (north or south) and which way round it goes. Where the diagram only shows a north line, add the angle and any other north lines yourself.
③ Bearings and trigonometryCalculator useful
The diagram shows the directions of the journey correctly, but the distances are not drawn to scale. There is a north line at A (the first question also has one at B to help you start). Add a north line at every other point you need and mark the angles. Find the angles inside the triangle, then use Pythagoras or trigonometry. Remember: a bearing is always measured clockwise from north.
Key steps
Elevation: the angle looking up from the horizontal. Depression: the angle looking down from the horizontal. They are equal (alternate angles).
Bearings are measured clockwise from north and are written with three figures, e.g. 045°, 270°.
Back bearing: add 180° if the bearing is less than 180°, otherwise subtract 180°.
Always draw a north line at each point of the journey and mark the angles before you calculate.
Rounding: give lengths correct to 3 significant figures and angles (and bearings from calculations) to 1 decimal place.