Triangle Trigonometry and Bearings
Select triangle area, sine rule or cosine rule and combine the result with three-figure bearing geometry.
How to study National 5 Mathematics
Secure one operational skill at a time, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and a checked conclusion.
Core concepts
Concept 1
Triangle area is ½ab sin C when C is the included angle between sides a and b.
Exam cue: Label side–opposite-angle pairs before choosing a rule.
Concept 2
The sine rule pairs each side with its opposite angle; the cosine rule handles three sides or two sides and their included angle.
Exam cue: Check that the angle in the area or cosine-rule substitution is included.
Concept 3
Bearings are measured clockwise from north and written as three figures, with diagrams supporting angle relationships.
Exam cue: Draw north lines and use parallel-line angle facts in bearing problems.
Risk pitfalls and guardrails
Pairing a side with a non-opposite angle in the sine rule.
Guardrail: Define directions and reference angles before beginning component or trigonometric work.
Using a non-included angle with two sides in the cosine rule.
Guardrail: Define directions and reference angles before beginning component or trigonometric work.
Measuring a bearing anticlockwise or from east.
Guardrail: Define directions and reference angles before beginning component or trigonometric work.
Memory anchors
Triangle area
A = ½ab sin C using the included angle C.
Sine rule
a/sin A = b/sin B = c/sin C.
Cosine rule for side
a² = b² + c² − 2bc cos A.
Cosine rule for angle
cos A = (b² + c² − a²)/(2bc).
Bearing
Clockwise from north, written with three digits.
Rule selection
Use known sides and angles to identify the complete usable pair or included angle.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Find the area of a triangle with sides 8 cm and 11 cm enclosing an angle of 30°.
Find the area of a triangle with sides 12 cm and 15 cm enclosing 60°, to 1 decimal place.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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