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Relations Between Sides and Angles of a Triangle — Syllabus

NIOS · Class 12 · Mathematics

What Relations Between Sides and Angles of a Triangle covers in NIOS Class 12 Mathematics: 4 topics, for the 2026-27 session.

45 questions25 flashcards3 formulas & key relations5 concepts

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4 Topics · NIOS Class 12 Mathematics · 2026-27

Topics in Relations Between Sides and Angles of a Triangle

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.

Key Concepts

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

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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.
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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