Right-Angled Triangles (OCR A Level Maths: Pure)

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Right-Angled Triangles

What is SOHCAHTOA?

  • SOH, CAH, and TOA are an easy way to remember the three basic trigonometry ratios
  • They show the relationship between an angle and the different sides of a right-angled triangle which we can label Hypotenuse, Adjacent and Opposite
  • We use them to find missing angles and sides for right‑angled triangles
    • Hypotenuse is the longest side of a right-angled triangle
    • Adjacent is the side next to the angle you are working with (in between the angle and the right angle)
    • Opposite is the side opposite the angle you are working with

Right-Angled Triangles Diagram 1, A Level & AS Level Pure Maths Revision Notes

  •  We use the inverse trig functions to find missing angles

Right-Angled Triangles Diagram 2, A Level & AS Level Pure Maths Revision Notes

How do I use SOHCAHTOA?

Right-Angled Triangles Diagram 3, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

  • Remember SOHCAHTOA are only for calculating missing sides and angles for right‑angled triangles
    • For non-right‑angled triangles you will need to use the Sine or Cosine rules.
  • Make sure your calculator is in degree mode (D).
  • Always check your answers are sensible…
    • Should my answer be longer or shorter than the sides I have already i.e. is it the hypotenuse?
    • Is my angle sensible…
    • Have I remembered to use -1?
  • Check if the question asks you to round your answer.

Worked example

Right-Angled Triangles Example Question, A Level & AS Level Pure Maths Revision Notes Right-Angled Triangles Example Solution, A Level & AS Level Pure Maths Revision Notes

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Lucy

Author: Lucy

Expertise: Head of STEM

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels. Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all. Lucy has created revision content for a variety of domestic and international Exam Boards including Edexcel, AQA, OCR, CIE and IB.