IGCSE Right Angled Trigonometry: Complete Guide for Cambridge IGCSE Mathematics

IGCSE right-angled trigonometry is a fundamental topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering SOHCAHTOA, finding missing sides and angles, and trigonometry formulas is essential for solving right-angled triangle problems.

This comprehensive IGCSE right-angled trigonometry guide covers everything you need to know, including SOHCAHTOA formulas, 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 SOHCAHTOA to find missing sides and angles in right-angled triangles, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Right Angled Trigonometry Matters

IGCSE right-angled trigonometry is an essential topic. Here’s why it’s so important:

• High frequency topic: Trigonometry questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for all trigonometry and geometry problems
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in construction, navigation, and engineering
• Problem-solving skills: Develops geometric reasoning and calculation abilities

Key insight from examiners: Students often confuse SOHCAHTOA formulas or make errors identifying opposite, adjacent, and hypotenuse. This guide will help you master these systematically.

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Understanding Right Angled Trigonometry

Right-angled trigonometry uses ratios of sides in right-angled triangles.

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SOHCAHTOA

SOH: Sin = Opposite / Hypotenuse CAH: Cos = Adjacent / Hypotenuse TOA: Tan = Opposite / Adjacent

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Finding Missing Sides

Example 1: Find side x in right-angled triangle. Angle = 30°, opposite = x, hypotenuse = 10.

Solution: Using SOH: sin(30°) = x / 10 0.5 = x / 10 x = 5

Answer: 5

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Finding Missing Angles

Example 2: Find angle θ. Opposite = 6, adjacent = 8.

Solution: Using TOA: tan(θ) = 6 / 8 = 0.75 θ = tan⁻¹(0.75) ≈ 36.87°

Answer: 36.87°

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Common Examiner Traps

• Formula confusion - Remember SOHCAHTOA correctly
• Side identification - Hypotenuse is always opposite right angle
• Calculator errors - Check calculator is in correct mode (degrees)

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Practice Questions

Question 1

Find side x. Angle = 45°, adjacent = x, hypotenuse = 12.

Solution: Using CAH: cos(45°) = x / 12 0.707 = x / 12 x ≈ 8.49

Answer: 8.49

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Tutopiya Advantage: Personalised IGCSE Right Angled Trigonometry Coaching

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Frequently Asked Questions About IGCSE Right Angled Trigonometry

What is SOHCAHTOA?

SOHCAHTOA is a mnemonic: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.

How do I find a missing side?

Identify which sides you have, choose correct formula (SOH, CAH, or TOA), substitute and solve.

How do I find a missing angle?

Use inverse trig functions: sin⁻¹, cos⁻¹, or tan⁻¹.

What is the hypotenuse?

The hypotenuse is the longest side, opposite the right angle.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Trigonometry: Complete SOHCAHTOA Guide - Master SOHCAHTOA
• IGCSE Sine Rule: Complete Guide - Master sine 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

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Next Steps: Master IGCSE Right Angled Trigonometry with Tutopiya

Ready to excel in IGCSE right-angled trigonometry? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
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• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master right-angled trigonometry and achieve your target grade.

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