IGCSE Sine Rule: Complete Guide for Cambridge IGCSE Mathematics

IGCSE sine rule is an essential trigonometry topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering sine rule formula, finding missing sides and angles, and sine rule applications is essential for solving non-right-angled triangle problems.

This comprehensive IGCSE sine rule guide covers everything you need to know, including the sine rule formula, when to use it, finding missing sides, finding missing angles, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to use the sine rule to find missing sides and angles in non-right-angled triangles, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Trigonometry practice deck featuring exam-style questions and instant feedback.

---

Why IGCSE Sine Rule Matters

IGCSE sine rule is an essential trigonometry topic. Here’s why it’s so important:

• High frequency topic: Sine rule questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for solving non-right-angled triangles
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in surveying, navigation, and engineering
• Problem-solving skills: Develops trigonometry and triangle-solving abilities

Key insight from examiners: Students often confuse when to use sine rule vs cosine rule or make calculation errors. This guide will help you master these systematically.

---

Understanding Sine Rule

Sine rule: a/sin(A) = b/sin(B) = c/sin(C)

Where:

• a, b, c are sides
• A, B, C are opposite angles

---

When to Use Sine Rule

Use when you have:

• Two angles and one side (AAS or ASA)
• Two sides and a non-included angle (SSA) - but be careful with ambiguous case

---

Finding Missing Sides

Example 1: Triangle ABC: angle A = 40°, angle B = 60°, side a = 8 cm. Find side b.

Solution: Using sine rule: a/sin(A) = b/sin(B) 8/sin(40°) = b/sin(60°) b = (8 × sin(60°)) / sin(40°) b = (8 × 0.866) / 0.643 ≈ 10.77 cm

Answer: 10.77 cm

---

Finding Missing Angles

Example 2: Triangle ABC: side a = 10 cm, side b = 12 cm, angle A = 50°. Find angle B.

Solution: Using sine rule: a/sin(A) = b/sin(B) 10/sin(50°) = 12/sin(B) sin(B) = (12 × sin(50°)) / 10 sin(B) = (12 × 0.766) / 10 = 0.919 B = sin⁻¹(0.919) ≈ 66.8°

Answer: 66.8°

---

Ambiguous Case (SSA)

When given two sides and a non-included angle, there may be two possible triangles.

---

Common Examiner Traps

• Formula errors - Remember: a/sin(A) = b/sin(B)
• Angle-side pairing - Side and its opposite angle must be paired
• Ambiguous case - Check if two solutions are possible

---

Practice Questions

Question 1

Triangle: angle A = 30°, angle B = 45°, side a = 6 cm. Find side b.

Solution: 6/sin(30°) = b/sin(45°) b = (6 × sin(45°)) / sin(30°) = (6 × 0.707) / 0.5 ≈ 8.49 cm

Answer: 8.49 cm

---

Tutopiya Advantage: Personalised IGCSE Sine Rule Coaching

• Live whiteboard walkthroughs of sine rule problems
• Exam-docket homework packs mirroring CAIE specimen papers
• Analytics dashboard so parents see accuracy by topic
• Flexible slots with ex-Cambridge markers for last-mile polishing

📞 Ready to turn shaky sine rule skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

---

Frequently Asked Questions About IGCSE Sine Rule

What is the sine rule?

Sine rule: a/sin(A) = b/sin(B) = c/sin(C) where sides and opposite angles are paired.

When do I use the sine rule?

Use when you have two angles and one side (AAS/ASA) or two sides and a non-included angle (SSA).

How do I find a missing side?

Use a/sin(A) = b/sin(B), rearrange to find the unknown side.

How do I find a missing angle?

Use a/sin(A) = b/sin(B), rearrange to find sin(angle), then use inverse sine.

---

Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Cosine Rule: Complete Guide - Master cosine rule
• IGCSE Area Rule: Complete Guide - Master area rule
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

---

Next Steps: Master IGCSE Sine Rule with Tutopiya

Ready to excel in IGCSE sine rule? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
• Progress tracking to identify and strengthen weak areas
• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master sine rule and achieve your target grade.

---