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Relations Between Sides and Angles of a Triangle — Concept Maps

NIOS · Class 12 · Mathematics

3 concept maps of Relations Between Sides and Angles of a Triangle for NIOS Class 12 Mathematics, each also written out as a text outline.

45 questions25 flashcards3 formulas & key relations5 concepts

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3 Concept Maps

Chapter Overview: Relations Between Sides and Angles of a Triangle

Chapter Overview: Relations Between Sides and Angles of a Triangle

The map in words

  • root((Triangle
  • Formulas))
    • Notation
      • BC = a opposite A
      • CA = b opposite B
      • AB = c opposite C
      • A plus B plus C = 180 deg
    • Sine Formula
      • a over sinA = b over sinB = c over sinC
      • Set equal to k
      • a = k sinA
      • b = k sinB
      • c = k sinC
      • Proof Uses Altitude
      • Three Cases
    • Cosine Formula
      • cosA = b sq + c sq minus a sq over 2bc
      • cosB = c sq + a sq minus b sq over 2ac
      • cosC = a sq + b sq minus c sq over 2ab
      • SSS Case
      • SAS Case
      • Special When A = 60 deg
        • b sq + c sq minus a sq = bc
    • Projection Formula
      • a = b cosC + c cosB
      • b = c cosA + a cosC
      • c = a cosB + b cosA
      • Geometric Meaning
      • Projection of Sides
    • Key Identities
      • sin sq A minus sin sq B
        • = sinA+B times sinA-B
      • B+C over 2 = 90 minus A over 2
      • sinB+C over 2 = cos A over 2
      • cosB+C over 2 = sin A over 2

Relations Between Sides and Angles - Complete Overview

Relations Between Sides and Angles - Complete Overview

The map in words

  • Triangle Relations
    • Sine Formula
      • Application: AAS, ASA cases
      • Form: a/sin A = b/sin B = c/sin C
      • Use: Find unknown sides from angles
      • Use: Find unknown angles from sides
    • Cosine Formula
      • Application: SSS, SAS cases
      • Form: cos A = (b² + c² - a²)/(2bc)
      • Check: Right angle detection
      • Use: Pythagorean generalization
    • Projection Formula
      • Application: Express sides
      • Form: a = b cos C + c cos B
      • Geometric: Projection interpretation
      • Derive: Foundation for Sine Formula
    • Triangle Elements
      • Sides: a, b, c
      • Angles: A, B, C
      • Constraint: A + B + C = π
      • Convention: Side opposite angle

Decision tree for choosing the right formula based on known information

Decision tree for choosing the right formula based on known information

The map in words

  • Know two angles and one side?
    • Yes: Use Sine Formula
      • Calculate missing side or angle
    • No: Know two sides and angle?
      • Between sides: Use Cosine Formula
      • Opposite to one side: Use Sine Formula

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Frequently Asked Questions

What are the important topics in Relations Between Sides and Angles of a Triangle for NIOS Class 12 Mathematics?
Key topics in Relations Between Sides and Angles of a Triangle include Standard Notation and Basic Concepts, Sine Formula (Law of Sines), Cosine Formula (Law of Cosines), Projection Formula. Study these first, then practise questions on each for the NIOS Class 12 board exam.
What do the concept maps for Relations Between Sides and Angles of a Triangle show?
The 3 maps show how the ideas in Relations Between Sides and Angles of a Triangle connect: Chapter Overview: Relations Between Sides and Angles of a Triangle; Relations Between Sides and Angles - Complete Overview. Each map is also written out as an outline on this page.
How should I revise Relations Between Sides and Angles of a Triangle for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Relations Between Sides and Angles of a Triangle. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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