Measuring angles and three-figure bearings · Foundation
導入済み| English | 意味 |
|---|---|
| bearing/ˈbeərɪŋ/ | 方位角 |
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.
Why is the reverse bearing of 070° equal to 250°?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The back bearing differs by exactly 180°: the parallel north lines at the two points make alternate angles equal. 360-70=290° confuses the reverse with the reflex complement.
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°.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
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°.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
320+180=500; subtract 360.
The reverse bearing of 070° is 290°.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
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.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Southeast is halfway from east 090° to south 180°.
Match each bearing convention to its rule.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
A bearing is always taken from the departure point, clockwise from north, with three digits.
Use this in your course
- 8300 · Foundation · 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.