Year 10: Bearings, elevation and depression

Bearings and vertical angles are common real-world trigonometry topics in Australian Year 10. They connect maps, navigation, surveying, and right-angled triangle calculations.

Bearings are measured clockwise from north, and angles of elevation or depression are measured from a horizontal line.

Work through the sections in order, then try the linked Year 10 skill quizzes after each section.

Reading a bearing

A three-figure bearing like $065 °$ means turn clockwise from north by $65 °$ . A bearing of $210 °$ points into the south-west quadrant.

Example 1: A ship travels on a bearing of

135 °

. Which direction is that close to?

Start at north.
Turn clockwise $135 °$ .
This points south-east.

Skill quiz: Measure a bearing from north

Practise measuring clockwise from north and writing bearings with three figures.

Calculations involving bearingsPremium

Angle of elevation

The angle of elevation is measured upward from a horizontal line. It is often used when looking up at a building, tree, or cliff.

Example 2: A student stands

20 m

from a flagpole. The angle of elevation to the top is

35 °

. Find the height of the flagpole.

Use $\tan θ = opposite / adjacent$ .
$\tan 35 ° = h / 20$ .
$h = 20 \tan 35 °$ .
$h \approx 14.0 m$ .

Skill quiz: Solve an elevation problem

Draw the horizontal line, label the opposite and adjacent sides, then choose a trigonometric ratio.

Angle of elevation and angle of depression

Angle of depression

The angle of depression is measured downward from a horizontal line. It often matches an angle of elevation because of alternate angles on parallel lines.

Example 3: From the top of a cliff, the angle of depression to a boat is

18 °

. The boat is

40 m

horizontally from the base of the cliff. Find the height of the cliff.

The angle of elevation from the boat is also $18 °$ .
Use $\tan 18 ° = h / 40$ .
$h = 40 \tan 18 ° \approx 13.0 m$ .

Skill quiz: Connect depression and elevation

Use the horizontal lines to identify equal angles before solving the right-angled triangle.

Angle of elevation and angle of depression

Common mistakes

Measuring bearings anticlockwise instead of clockwise.
Starting the bearing from east or west instead of north.
Confusing the horizontal side and the sloping line in elevation questions.

Skill quizzes: Check directions and side labels

Review the north line in bearings and the horizontal reference line in elevation and depression questions.