Geometry and Trigonometry
Geometry and Trigonometry tests spatial reasoning and precise use of angle, length and area relationships. Expect angle facts, triangles and polygons, Pythagoras’ theorem, right-triangle trigonometry, bearings, similarity, and the mensuration of common plane and solid shapes.
Core rules and concepts
- Angles on a straight line sum to 180°; angles around a point sum to 360°; vertically opposite angles are equal.
- The interior angles of a triangle sum to 180°. For an n-sided polygon, the interior angle sum is (n − 2) × 180°.
- Pythagoras: in a right-angled triangle, a² + b² = c², where c is the hypotenuse.
- Trigonometry: sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent.
- Bearings are measured clockwise from north, written with three digits, for example 047°.
- Similar shapes have equal angles and proportional corresponding sides; area scale factor = (length scale factor)².
- Volume of a prism = area of cross-section × length.
Worked example
A ladder 6 m long leans against a wall and makes 70° with the ground. How high up the wall does it reach? The wall height is opposite the 70° angle, and the ladder is the hypotenuse. sin 70° = h/6, so h = 6 sin 70° ≈ 6 × 0.9397 = 5.64 m. The ladder reaches about 5.64 m up the wall.
Traps that cost marks
Using the wrong side as opposite or adjacent; using Pythagoras in a non-right triangle; measuring a bearing anticlockwise or from the wrong north line; rounding too early in a multi-step calculation; and confusing length scale factor with area scale factor.