MathematicsChapter 6: Trigonometry and Bearing
Bearings From North
A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
Learning objectives
- Explain bearings from north in clear mathematical language
- Apply the ideas in three-figure bearings
- Solve problems involving using a sketch
Definition
A bearing is a compass direction, usually a three-figure angle measured from North clockwise. North itself is 000, East is 090, South is 180, and West is 270. The bearing of B from A is the direction you would travel from A toward B. Keep three digits even for small angles: write 075, not 75 deg, when the question asks for a three-figure bearing.
Where / symbols
- three-figure
- A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
- from North
- A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
- clockwise
- A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
- 000
- North itself is 000, East is 090, South is 180, and West is 270.
Overview
North is the zero; the clock turns the other way from standard position:
Three-Figure Bearings
Stand at the starting point, face North, then turn clockwise until you face the target. The turning angle, written with three digits, is the bearing. 000 is North, 090 is East, 180 is South, and 270 is West. A ship on bearing 045 is heading north-east. Because clockwise from North is not the same as anti-clockwise from the x-axis, do not treat a bearing as a standard-position angle without a sketch.
Examples 000 North · 090 East · 180 South
Using A Sketch
Draw North as an upward arrow. From that arrow, swing clockwise to the path. If a road runs due east of a town, its bearing from the town is 090. If you reverse the journey, the back bearing differs by 180 (add or subtract 180 to stay between 000 and 360). Acute bearings such as 030 still need three figures.
Examples Town to a point due east: 090 · Bearing 030 still written 030 · Back of 090 is 270
What it means
A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
Main ideas
1. THREE-FIGURE BEARINGS: Stand at the starting point, face North, then turn clockwise until you face the target. 2. USING A SKETCH: Draw North as an upward arrow.
Why it matters
Trigonometry enters when a right triangle is drawn against North and East. The angle with North is the bearing if you turned clockwise; tan of the other angle may give East-West against North-South. Always label North on the diagram before you compute tan theta.
How to answer in an exam
Bearings in this course are three-figure from North clockwise: 000 North, 090 East. Standard-position theta starts from the positive x-axis anti-clockwise, so a bearing of 090 is not a 90 deg standard angle without a fresh sketch. Write three digits.
Explanation
Trigonometry enters when a right triangle is drawn against North and East. The angle with North is the bearing if you turned clockwise; tan of the other angle may give East-West against North-South. Always label North on the diagram before you compute tan theta.
In simple words
Bearings in this course are three-figure from North clockwise: 000 North, 090 East. Standard-position theta starts from the positive x-axis anti-clockwise, so a bearing of 090 is not a 90 deg standard angle without a fresh sketch. Write three digits.
Key points
- three-figure
- from North
- clockwise
- 000
- face North
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Bearings From North
Sticky Notes · Quick Revision
Core Idea
- A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
Key Terms
- three-figure: A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
- from North: A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
Main Pattern
- 1. THREE-FIGURE BEARINGS: Stand at the starting point, face North, then turn clockwise until you face the target.
- 2. USING A SKETCH: Draw North as an upward arrow.
Worked Reminder
- 000 North
- 090 East
- 180 South
Common Mistake
- Bearings in this course are three-figure from North clockwise: 000 North, 090 East. Standard-position theta starts from the positive x-axis anti-clockwise, so a bearing of 090 is not a 90 deg standard angle without a fresh sketch. Write three digits.
Exam Tip
- State the rule for bearings from north, show each algebraic step, and check the final answer against the question.
60-second revision
- A bearing is a compass direction, usually a three-figure angle measured from North clockwise.
- Stand at the starting point, face North, then turn clockwise until you face the target.
- Draw North as an upward arrow.
- Trigonometry enters when a right triangle is drawn against North and East.
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