C.1 Geometry and Trigonometry
3D geometry — distance, midpoint, surface area, volume of solids; angles between lines and planes. The full triangle toolkit: SOH-CAH-TOA, sine and cosine rules, and triangle area. Real applications — bearings, angles of elevation/depression. Circle arc length and sector area. Voronoi diagrams for nearest-neighbour interpolation — the spatial-AI showpiece of the syllabus.
3D geometry — distance, midpoint, volume, surface areaSign up
3D distance and midpoint · Volume and surface area of standard solids · Angles in 3D
Sine, cosine, tangent ratios; sine and cosine rules; triangle areaSign up
SOH-CAH-TOA · Sine rule and cosine rule · Area = ½ab sin C
Triangle applications — elevation, depression, bearingsSign up
Angles of elevation and depression · Bearings
Circle arc length and sector areaSign up
Arc length L = θ/360 × 2πr · Sector area A = θ/360 × πr²
Perpendicular bisector equationsSign up
Midpoint and slope of perpendicular · Equation of the bisector
Voronoi diagrams and nearest-neighbour interpolationSign up
Voronoi cells from perpendicular bisectors · Toxic-waste / nearest-shop / mobile-cell applications