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Revision Notes

Relations Between Sides and Angles of a Triangle

NIOS · Class 12 · Mathematics

Quick revision notes for Relations Between Sides and Angles of a Triangle — NIOS Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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Key Topics to Revise

1

Standard Notation and Basic Concepts

  • In triangle ABC, angles are denoted by A, B, C at the respective vertices.
  • Sides opposite to angles A, B, C are denoted by a, b, c respectively. So BC = a, CA = b, AB = c.
  • A + B + C = 180° (or π radians) — this is used very frequently in proofs.
2

Sine Formula (Law of Sines)

  • The Sine Formula states that in any triangle, sides are proportional to the sines of their opposite angles.
  • It holds for ALL types of triangles: acute, right-angled, and obtuse.
  • The proof uses the altitude (perpendicular) from one vertex to the opposite side, considering all three cases of the opposite angle.
3

Cosine Formula (Law of Cosines)

  • The Cosine Formula expresses each side of a triangle in terms of the other two sides and the included angle.
  • It is derived using the Pythagorean theorem applied to the altitude from a vertex, for all three cases (acute, right, obtuse angle).
  • There are three versions — one for each angle A, B, C.
4

Projection Formula

  • The Projection Formula expresses each side of a triangle as a sum of projections of the other two sides onto it.
  • It is proved by dropping an altitude from A to BC and applying trigonometric ratios, for all three cases of the angle (acute, right, obtuse).
  • There are three versions: a = b cosC + c cosB; b = c cosA + a cosC; c = a cosB + b cosA.

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Full Notes

Key Concepts

The Sine Formula states thatThe Cosine Formula provides three relationshipsThe Projection Formula statesEvery triangle has six elementsThere are four main cases

Frequently Asked Questions

What are the important topics in Relations Between Sides and Angles of a Triangle for NIOS Class 12 Mathematics?
Relations Between Sides and Angles of a Triangle covers several key topics that are frequently asked in NIOS Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Relations Between Sides and Angles of a Triangle — NIOS Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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