Unit 2 – Non-calculator (geometry focus) · Both
Geometry Essentials – Angles, Pythagoras & Trigonometry
Key geometry skills tested heavily in Unit 2 and also in Unit 3.
Geometry has a strong presence in the non-calculator paper. Know your angle facts, area formulae and Pythagoras cold.
Essential angle facts
• Angles on a straight line sum to 180°
• Angles around a point sum to 360°
• Vertically opposite angles are equal
• Triangle angles sum to 180°
• Parallel lines: corresponding equal, alternate equal, co-interior sum to 180°
Pythagoras’ Theorem
In a right-angled triangle: a² + b² = c²
where c is the hypotenuse.
To find a shorter side: a² = c² − b²
Worked example
A right-angled triangle has shorter sides 5 cm and 12 cm. Find the hypotenuse.
Solution
c² = 25 + 144 = 169 c = √169 = **13 cm**
Trigonometry (Higher) – SOH CAH TOA
sin θ = Opposite / Hypotenuse
cos θ = Adjacent / Hypotenuse
tan θ = Opposite / Adjacent
Worked example
Side opposite 35° is 8 cm. Find the hypotenuse (1 d.p.).
Solution
sin 35° = 8 / hyp hyp = 8 / sin 35° ≈ **13.9 cm**
Practice questions
Try these without looking at the answers first.
Q1.Shorter sides 9 cm and 12 cm. Find the hypotenuse.
Show answer
15 cm
Q2.Opposite a 42° angle, hypotenuse 20 cm. Find opposite side (1 d.p.).
Hint: opp = hyp × sin 42°
Show answer
13.4 cm