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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.

45 questions25 flashcards5 concepts

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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?
Key topics in Relations Between Sides and Angles of a Triangle include Chapter Overview: Relations Between Sides and Angles of a Triangle, Relations Between Sides and Angles - Complete Overview, Decision tree for choosing the right formula based on known information. These are the concepts NIOS Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Relations Between Sides and Angles of a Triangle — NIOS Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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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