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.
Practice lesson for the WJEC Mathematics and Numeracy Double Award. This is not an official WJEC page.
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