Trigonometry (SOHCAHTOA)
AQA Mathematicsintermediate⭐ High PriorityYears 10-11
What You Need to Know
- SOH CAH TOA — three ratios for right-angled triangles
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
- tan θ = opposite / adjacent
- Use the inverse functions (sin⁻¹, cos⁻¹, tan⁻¹) to find angles
Finding a Side
Label the sides relative to the angle you know, pick the right ratio, and solve.
Worked Example
Find x: angle = 35°, hypotenuse = 12cm, x is opposite the angle
We have the opposite and hypotenuse → use sinsin(35°) = x / 12x = 12 × sin(35°) = 12 × 0.5736 = 6.88
Answer: x = 6.88cm (3 s.f.)
Common Mistakes
- Labelling sides wrong — 'opposite' and 'adjacent' depend on which angle you're using
- Calculator in the wrong mode (must be in degrees)
- Using sin when you should use cos — always label sides first
Exam Tips
- Draw the triangle and label O, A, H before picking your ratio
- For non-right-angled triangles, you'll need the Sine Rule or Cosine Rule (higher tier)
Related Topics
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