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Cosine Law
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
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Cosine Law
What is it?
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
In simple words
- Two sides and included angle, or three sides.
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
Important terms
Cosine Law: Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
What you should learn
- Define and explain cosine law.
- Apply cosine law to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Examples
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
CORE UNDERSTANDING
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 10
Full school-level explanation
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
Learn the idea, then use it:
WHAT — COSINE LAW
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
CORE UNDERSTANDING
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
Remember
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
Examples
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
- COSINE LAW: Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
- keep the ideas separate
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
- correct term
Deeper understanding
Go beyond memorising Cosine Law. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
- keep the ideas separate
- Cosine Law: Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not
- WHAT — COSINE LAW: Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not
Do not merge cosine law with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Cosine Law: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
- keep the ideas separate
Important formulas
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
Common exam traps
- Do not merge cosine law with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge cosine law with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge cosine law with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
included angle or SSS
a/sin A = b/sin B
c2 = a2+b2-2ab cos C
keep the ideas separate
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
a/sin A = b/sin B
- Definition
- Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
- Formula
- a/sin A = b/sin B
- Example
- included angle or SSS
- Critical warning
- Do not merge cosine law with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Cosine Law.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Cosine Law and say why it fits.
Mistake
Q4. State one common mistake students make about Cosine Law.
Exam note
Q5. Write a short exam note on Cosine Law: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.