IB MYP 4-5 Maths- Bearings- Study Notes - New Syllabus
IB MYP 4-5 Maths- Bearings – Study Notes
Standard
- Bearings
Bearings
Bearings
A bearing is the clockwise angle measured from the North direction to a line connecting two points. Bearings are used to describe directions in navigation, surveying, and mapping.
Key Features of Bearings:
- Measured in degrees from the North direction.
- Always measured clockwise.
- Represented as a three-digit number (e.g., 045°, 120°, 270°).
- North is the reference line (0° or 360°), East = 90°, South = 180°, West = 270°.
Important Points:
- Bearings are usually written as three digits: for example, 30° → 030°.
- The bearing of point B from point A is different from the bearing of point A from point B.
- Bearings often involve angle of elevation/depression problems combined with trigonometry.
Types of Bearings:
- True Bearings: Measured from North in a clockwise direction.
- Compass Bearings: Expressed in terms of North or South followed by an angle and East or West (e.g., N30°E).
Steps to Solve Bearings Problems:
- Draw a clear diagram with North direction at the reference point.
- Mark the given bearing and measure clockwise from North.
- Apply trigonometry (sine, cosine, tangent) or Pythagoras if distances are involved.
- For reverse bearings, add/subtract 180° (keeping within 0°–360°).
Example :
A ship sails from point A to point B on a bearing of 140° for 10 km. Draw a diagram showing the route.
▶️ Answer/Explanation
Draw North at point A, then measure 140° clockwise from North. Draw a line 10 km long to point B. This shows the route with a bearing of 140°.
Example :
A ship sails 8 km from port A on a bearing of 045° to point B. Then it sails 6 km east to point C. Find the bearing of C from A.
▶️ Answer/Explanation
Step 1: Draw North at A. Mark AB at 045° (northeast direction, 8 km). From B, draw BC horizontally east (6 km).
Step 2: Join AC and calculate angle using trigonometry:
Using cosine rule or vector approach:
\( \tan \theta = \dfrac{\text{East distance}}{\text{North distance}} \) after calculating AC.
Step 3: Add angle to 0° North to get bearing.
Final Answer: Bearing of C from A ≈ 064°.
Example :
A helicopter leaves an airport and flies 12 km on a bearing of 135°, then changes direction and flies 9 km on a bearing of 045°. Find the distance and bearing from the starting point to the final position.
▶️ Answer/Explanation
Draw the route and resolve into components:
First leg (135°): South-East → components = (12 sin 45°, 12 cos 45°) = (8.49, 8.49).
Second leg (045°): North-East → components = (9 sin 45°, 9 cos 45°) = (6.36, 6.36).
Total East displacement: 8.49 + 6.36 = 14.85 km.
Total North displacement: -8.49 + 6.36 = -2.13 km (so slightly south).
Distance = \( \sqrt{(14.85)^2 + (2.13)^2} \approx 15.0 \) km.
Bearing = arctan(14.85 / 2.13) from South → adjust for North reference = about 082°.
Final Answer: Distance ≈ 15 km, bearing ≈ 082°.