SOHCAHTOA: Year 9 Trigonometry Guide
30 October 2026 · Pi Leo Academy
SOHCAHTOA looks like a word to memorise, but its real job is simple: it helps you choose a ratio for a right-angled triangle. Once you label the sides correctly, finding a missing length becomes a series of small, explainable steps.
This Year 9 lesson introduces sine, cosine and tangent through clear examples. Keep a pencil and a calculator in degree mode nearby, and pause the video before each solution.
Watch the lesson
Watch this Pi Leo Academy lesson on YouTube. Pause whenever you want to try a step yourself.
Label the sides before choosing a formula
First mark the acute angle you are using. The side names depend on that choice:
- Hypotenuse: opposite the right angle; it is the longest side.
- Opposite: directly across from your chosen acute angle.
- Adjacent: next to that angle, excluding the hypotenuse.
If you switch to the other acute angle, opposite and adjacent swap. The hypotenuse stays the same.
What SOHCAHTOA tells you
- SOH: sin θ = opposite ÷ hypotenuse.
- CAH: cos θ = adjacent ÷ hypotenuse.
- TOA: tan θ = opposite ÷ adjacent.
For example, if opposite = 3, adjacent = 4 and hypotenuse = 5, then sin θ = 3/5. Enlarge every side by a factor of 2 and the ratio becomes 6/10, still 3/5. Similar right triangles have matching angles and matching ratios, even when their sizes differ.
Worked example: find a missing opposite side
A right triangle has a hypotenuse of 12 cm and an acute angle of 30°. Let x be the side opposite 30°.
- We know the hypotenuse and need the opposite side, so choose sine.
- Write sin 30° = x ÷ 12.
- Multiply both sides by 12: x = 12 × sin 30°.
- Since sin 30° = 0.5, x = 6 cm.
The answer makes sense because a leg must be shorter than the hypotenuse. Writing the equation before using the calculator also helps you see what each number represents.
Avoid these common mix-ups
Do not label “opposite” by where a side sits on the page: always use the chosen angle. Check that the triangle has a right angle, set your calculator to DEG for angles measured in degrees, and round at the end of the calculation.
Revisit the reasoning in the trigonometric ratios study note before moving on to harder diagrams.
Try these two questions
- A right triangle has an angle of 20° and an adjacent side of 5 cm. Find the opposite side to one decimal place.
- A right triangle has a hypotenuse of 10 cm and an angle of 60°. Find the side adjacent to 60°.
Answers: 1. Use tangent: opposite = 5 × tan 20° ≈ 1.8 cm. 2. Use cosine: adjacent = 10 × cos 60° = 5 cm.
Your matching study notes
Use these notes alongside the video to revisit the method and practise at your own pace. Full notes and PDF downloads require an eligible Pi Leo Academy membership and sign-in.
- Year 9: why trigonometric ratios stay constant — VC2M9SP01 · Download the member study-note PDF
- Year 9: choosing a spatial method — VC2M9M03 · Download the member study-note PDF
Take the next triangle with a clear method
Understanding one example is a start; choosing the right ratio independently takes practice. Subscribe to Pi Leo Academy for more topic notes, worked examples and practice. Use the notes to revisit the method, then tackle the next question with a plan.
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