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Corbett MathsTrigonometry — SOH CAH TOA
Corbett MathsSine rule and cosine rule
GCSE Maths TutorThe Cosine Rule | Grade 7 Maths Revision | GCSE Maths Tutor
Key facts & methods
Right-angled triangle trigonometry
- Pythagoras: a² + b² = c² (c is hypotenuse). Find missing side: c = √(a²+b²), a = √(c²−b²).
- SOH CAH TOA: sin θ = opp/hyp. cos θ = adj/hyp. tan θ = opp/adj.
- Finding angle: use inverse function. θ = sin⁻¹(opp/hyp) etc.
- Angles of elevation (looking up) and depression (looking down) — both measured from horizontal.
- 3D Pythagoras: find diagonal of cuboid = √(l²+w²+h²). Or apply twice.
Sine rule and cosine rule
- Sine rule: a/sin A = b/sin B = c/sin C. Use when you have a side and its opposite angle.
- Use for: (i) two angles + one side. (ii) two sides + one non-included angle (watch for ambiguous case).
- Cosine rule: a² = b² + c² − 2bc cos A. Use when you have two sides and the included angle, or all three sides.
- Rearranged to find angle: cos A = (b²+c²−a²)/(2bc).
- Area of any triangle: Area = ½ab sin C (a,b are two sides, C is included angle).
Exam questions — 5 questions · 14 marks · Edexcel 4MA1 style
⚡ Show ALL working — the AI awards method marks just like a real examiner. Partial credit for correct working even if the final answer is wrong.
3 marksPythagoras and trig4MA1 style 🔢 Calculator
A right-angled triangle has legs of length 7 cm and 9 cm. (a) Find the hypotenuse to 2 d.p. (b) Find the smallest angle in the triangle. (3 marks)
Hint: (a) Pythagoras: c² = a²+b². (b) Smallest angle is opposite the shortest side (7cm). Use sin θ = opp/hyp or tan θ = opp/adj.
+30 XP
3 marksSine rule4MA1 style 🔢 Calculator
In triangle ABC, angle A = 34°, angle B = 72°, and side b = 14.5 cm. Find side a. Give your answer to 3 significant figures. (3 marks)
Hint: Find angle C first (angles sum to 180°). Apply sine rule: a/sin A = b/sin B. Cross-multiply to find a.
+30 XP
3 marksCosine rule — find angle4MA1 style 🔢 Calculator
A triangle has sides 8 cm, 11 cm and 14 cm. Find the largest angle. Give your answer to 1 decimal place. (3 marks)
Hint: Largest angle is opposite the longest side. Use rearranged cosine rule: cos A = (b²+c²−a²)/(2bc). A negative value means an obtuse angle.
+30 XP
3 marksArea of triangle4MA1 style 🔢 Calculator
Two sides of a triangle are 7 cm and 10 cm. The angle between them is 63°. Calculate the area of the triangle. (3 marks)
Hint: Area = ½ab sin C. The angle C must be the angle BETWEEN the two given sides (the included angle).
+30 XP
1 mark3D Pythagoras4MA1 style
A cuboid has dimensions 3 cm × 4 cm × 12 cm. What is the length of the longest diagonal?
A 13 cm
B 19 cm
C 15 cm
D 7 cm
Module complete! 🎉
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