Mastering the Cosine Rule: Step-by-Step Guide
Hello students! As your math teacher, I know that moving beyond right-angled triangles can feel tricky. While Pythagoras works for 90-degree triangles, the Cosine Rule is your "Master Key" for any triangle! Whether you are preparing for GCSE, IGCSE, or O-Levels, this rule is a must-know.
🎥 Watch My Detailed Video Lesson
Before jumping into the worksheet, watch me solve these problems step-by-step.
▶️ CLICK HERE TO WATCH VIDEOWhat is the Cosine Rule?
The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles. It is essential when you have SAS (Side-Angle-Side) or SSS (Side-Side-Side).
a² = b² + c² - 2bc cos(A)
Practice Worksheet
Ready to test your skills? I have prepared a comprehensive worksheet for you. You can view it below or download it for your practice.
Real-Life Application
Did you know engineers use the Cosine Rule to design bridges? It helps calculate the length of supporting beams when the angles between them are not 90 degrees.
📝 Quick Worked Example
Find side 'a' if b=8, c=10, and Angle A=60°:
a² = 8² + 10² - 2(8)(10) cos(60°)
a² = 64 + 100 - 160(0.5) = 164 - 80 = 84
a = √84 ≈ 9.17
💡 Exam Tips
- Ensure your calculator is in DEG mode.
- Remember: side 'a' is ALWAYS opposite Angle 'A'.
- Write down the formula before you start—it often earns you a mark!
