Skip to main content
Super TutorResources
Chapter 5 of 38
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Syllabus

Relations Between Sides and Angles of a Triangle

NIOS · Class 12 · Mathematics

Complete topic list for Relations Between Sides and Angles of a Triangle in NIOS Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

5 concepts

Interactive on Super Tutor

Studying Relations Between Sides and Angles of a Triangle? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for syllabus and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

4 Topics · NIOS Class 12 Mathematics

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

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.

More resources for Relations Between Sides and Angles of a Triangle

All 38 chapters — NIOS Class 12 Mathematics Syllabus

For serious students

Get the full Relations Between Sides and Angles of a Triangle chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for NIOS Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free