Last reviewed: 10 November 2026
Updated November 2026. These Grade 9 bearings and angles of elevation notes cover compass and true bearings, finding the bearing of one point from another, locating points by bearing and distance, angles of elevation and depression, and simple surveying with scale drawings. A true bearing is measured clockwise from north and written with three digits, so east is 090° and south-west is 225°. The angle of elevation is measured upwards from the horizontal; the angle of depression is measured downwards.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub.
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What the Grade 9 Curriculum Covers
Scale drawing is a sub-strand under Geometry in the Kenya Institute of Curriculum Development’s Grade 9 Mathematics design. It covers compass and true bearings, the bearing of a point, locating a point using bearing and distance, angles of elevation and depression, and simple surveying. The design is listed on the KICD Grade Nine curriculum designs page.
Compass Bearings and True Bearings
- Compass bearings start from north or south and turn towards east or west, with an angle up to 90°: N30°E, S45°W.
- True bearings are measured clockwise from north, from 000° to 360°, always with three digits: N30°E = 030°, S45°W = 225°, N60°W = 300°.
Converting compass to true bearings
| Compass bearing | True bearing |
|---|---|
| N x°E | x° |
| S x°E | 180° − x° |
| S x°W | 180° + x° |
| N x°W | 360° − x° |
Bearing of One Point From Another
“The bearing of B from A” means stand at A, face north, and turn clockwise to face B. The back bearing (A from B) differs by 180°: if B is on 060° from A, then A is on 240° from B.
Locating a Point by Bearing and Distance
Worked example
A learner walks 4 km on a bearing of 090° (due east), then 3 km on 000° (due north). Using a scale of 1 cm to 1 km:
- Draw a north line at the start, S. Draw 4 cm due east to P.
- At P draw a north line and measure 3 cm north to Q.
- Join S to Q and measure: 5 cm, so the learner is 5 km from the start.
- Measure the angle at S clockwise from north to SQ: about 53°. The bearing of Q from S is about 053°.
This right-angled case can be checked with Pythagoras (3² + 4² = 5²) and with trigonometry, but in scale-drawing questions, measured answers are accepted within a small tolerance.
Angles of Elevation and Depression
- Angle of elevation: looking up at an object, the angle between the horizontal and your line of sight.
- Angle of depression: looking down, the angle between the horizontal and your line of sight.
The angle of elevation of A from B equals the angle of depression of B from A, because they are alternate angles between parallel horizontal lines. These definitions match those used in OpenStax Algebra and Trigonometry’s section on right triangle trigonometry.
Worked example: height of a flagpole by scale drawing
From a point 20 m from the foot of a flagpole on level ground, the angle of elevation of the top is 30°. Using 1 cm to 2 m: draw a 10 cm base, measure 30° at the observer’s end, and draw a vertical line at the pole’s end. Where they meet, measure the height: about 5.8 cm, so the pole is about 11.5 m tall. (Trigonometry gives 20 × tan 30° ≈ 11.55 m.)
Worked example: angle of depression
From the top of a 40 m cliff, a boat is seen at an angle of depression of 30°. The angle of elevation of the cliff top from the boat is also 30°. Scale drawing (or 40 ÷ tan 30°) gives the boat about 69 m from the foot of the cliff.
Simple Surveying
To map a small plot, pick a baseline, measure distances along it, and measure offsets at right angles to features such as corners or trees. Plot them to scale to draw the plot and estimate its area. The curriculum suggests doing this in the school compound.
Original Practice Questions With Worked Answers
- Write S20°E as a true bearing. 180 − 20 = 160°.
- Write 310° as a compass bearing. N50°W.
- The bearing of P from Q is 125°. Find the bearing of Q from P. 125 + 180 = 305°.
- The angle of elevation of a roof from the ground is 40°. What is the angle of depression of that point on the ground from the roof? 40°.
- Using 1 cm to 5 m, how long is a line representing 35 m? 7 cm.
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is a true bearing?
An angle measured clockwise from north, written with three digits, such as 045° or 270°.
How do you find a back bearing?
Add 180° if the bearing is less than 180°, or subtract 180° if it is 180° or more.
What is the difference between angles of elevation and depression?
Elevation is measured upwards from the horizontal; depression is measured downwards. For two points, they are equal.
Why do we use scale drawing for bearings?
It lets us find distances and directions that cannot be measured directly, by drawing them accurately to a smaller size.