This topic summary covers Knowledge Organiser: Trigonometry — SOH CAH TOA within Trigonometry (SOH CAH TOA) for GCSE Mathematics. Revise Trigonometry (SOH CAH TOA) in Geometry & Measures for GCSE Mathematics with 19 exam-style questions and 7 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Trigonometry — SOH CAH TOA
Key Terms
- Hypotenuse (H): Longest side, opposite the right angle
- Opposite (O): Side opposite the angle you are working with
- Adjacent (A): Side next to the angle (not the hypotenuse)
- Inverse trig: sin⁻¹, cos⁻¹, tan⁻¹ — used to find angles
Must-Know Facts
- Only works for RIGHT-ANGLED triangles
- Label O, A, H from the angle you are working with — not from the right angle
- Calculator MUST be in DEGREE mode (test: sin 30° = 0.5)
- To find a side: rearrange the trig formula
- To find an angle: use the inverse function (SHIFT + sin/cos/tan)
Key Formulas
- SOH: sin θ = O ÷ H
- CAH: cos θ = A ÷ H
- TOA: tan θ = O ÷ A
- Find side: O = H × sin θ, A = H × cos θ, O = A × tan θ
- Find angle: θ = sin⁻¹(O/H), cos⁻¹(A/H), tan⁻¹(O/A)
Common Mistakes
- Labelling sides from the wrong angle: O, A, H are always relative to the angle θ being used — relabel if the angle changes
- Using sin when should use cos (or vice versa): Check which sides are known/needed — O&H → sin; A&H → cos; O&A → tan
- Finding angle vs finding side: To find a side, multiply; to find an angle, use the inverse function (sin⁻¹ etc.)
- Calculator in wrong mode: Always use DEGREE mode for GCSE — check the display shows D not R or G
Practice questions for Trigonometry (SOH CAH TOA)
Which trigonometric ratio connects the opposite side and the hypotenuse in a right-angled triangle?
For the triangle shown, a student chooses to use sin to find the missing side. Explain why they chose sin rather than one of the other trigonometric ratios.