Measuring angles and three-figure bearings · Higher
| English | 中文 | Pinyin |
|---|---|---|
| bearing/ˈbeərɪŋ/ | 方位角 | fāng wèi jiǎo |
A walking route has bearing 070° from A to B. Turning around changes the reference point and reverses the direction; it does not keep the same bearing.
- A walking route has bearing 070° from A to B. Turning around changes the reference point and reverses the direction; it does not keep the same bearing.
- This lesson studies bearing 方位角: A direction measured clockwise from north at the starting point.
Choose the mathematical structure
- Draw a north line at the starting point, then measure clockwise to the route. Write three digits: east 090°, south 180°, west 270°, north 000°. NE, SE, SW and NW are 045°,135°,225°,315°. For the reverse bearing add 180° and reduce modulo 360°. Use a ruler for a stated-scale length and the correct protractor scale for a stated angle.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines bearing?
A direction measured clockwise from north at the starting point.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
From A to B the bearing 070° is 70° clockwise from north. From B to A it is 070+180=250°. A bearing of 320° reverses to 500-360=140°. East is 090°, not 90 without its three-digit form. A route bearing 120° points southeast of the starting point, making 30° below east. On a 1:10000 map, a 3 cm route represents 300 m; to construct bearing 120°, place the protractor centre at the route start, align its zero with north and measure clockwise. Keep the ruler scale and angular direction as separate decisions.
Measuring angles and three-figure bearings
Draw a north line at the starting point, then measure clockwise to the route
Classify the worked-case statements, then explain the units or invariant that justifies each decision.
Find the reverse bearing of 070°.
070+180=250°.
Test a tempting shortcut
- A bearing is measured at the departure point, not the destination. Read clockwise from north rather than the acute angle to the nearest compass axis. The back bearing differs by 180°, even when the diagram is oblique.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The reverse bearing of 070° is 290°. This claim is false. Explain which definition or assumption it violates.
Find the reverse bearing of 320°.
320+180=500; subtract 360.
The reverse bearing of 070° is 290°.
A bearing is measured at the departure point, not the destination. Read clockwise from north rather than the acute angle to the nearest compass axis. The back bearing differs by 180°, even when the diagram is oblique.
Interpret a new situation
- AQA G15 includes measured lengths/angles, maps, the eight compass directions and three-figure bearings. State which point supplies north and distinguish a numerical bearing from a measured scale distance.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Give the bearing of southeast in degrees.
Southeast is halfway from east 090° to south 180°.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Higher · 3.4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A direction measured clockwise from north at the starting point. Choose the relationship, show the method, check its assumptions and interpret the result.