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Want to master three-dimensional geometry for your KCSE or high school exams? 📐 In this video, we tackle a complex geometry problem involving a cuboid, using trigonometry, Pythagoras' Theorem, and the cosine rule to calculate lengths, angles, and the angle between planes. 👨🏫 Perfect for KCSE candidates, form 3 and form 4 students, and anyone reviewing advanced geometry! 🔍 What you'll learn: How to find the length of a diagonal using sine. Applying cosine rule in non-right-angled triangles. Finding angles between two planes in 3D geometry. How to visualize geometry problems step by step. 📊 Real KCSE-style question broken down in full! Timestamps: 0:00 - Introduction to 3D Geometry Problem 0:12 - Understanding the Cuboid and Diagonals 0:55 - Part A: Finding X using sine rule 2:15 - Step-by-step trigonometric ratios explained 3:50 - Final answer for X 4:05 - Part B: Finding angle ∠CAE using cosine rule 6:00 - Why we apply cosine rule (not SOHCAHTOA) 8:04 - Using Pythagoras to find missing sides 11:00 - Final length of AE calculated 12:00 - Substituting into cosine rule to find angle 14:22 - Final answer for ∠CAE 14:40 - Part C: Angle between planes BCM and EFGH 15:30 - Visualizing intersecting planes 17:03 - Applying cosine to find angle between planes 19:20 - Final answer for angle between planes 19:45 - Conclusion & Final Remarks 💡 Don't forget to like, share, and subscribe for more detailed walkthroughs on mathematics and physics. ✅ Subscribe for more: [Insert your channel link] #MathMadeEasy #GeometryTutorial #KCSEMath #3DGeometry #HighmarkMPTutor #3DGeometry #KCSEMath #Trigonometry #MathTutorial #MathsFormFour #HighmarkMPTutor #CosineRule #MathKenya #GeometryMadeEasy