Year 10 trigonometry SOHCAHTOA helps students choose sine, cosine or tangent when working with right-angled triangles. The most important first step is to label the sides relative to the angle you are using, then select the correct ratio.
Year 10 trigonometry SOHCAHTOA: what to know
This practical guide explains Year 10 trigonometry SOHCAHTOA through examples, checks and realistic next steps for students and parents.
What SOHCAHTOA means
| Memory aid | Formula |
|---|---|
| SOH | sin θ = opposite ÷ hypotenuse |
| CAH | cos θ = adjacent ÷ hypotenuse |
| TOA | tan θ = opposite ÷ adjacent |
The hypotenuse is always opposite the right angle. Opposite and adjacent depend on which acute angle is being considered.
Example 1: find the opposite side
In a right triangle, angle θ = 30° and hypotenuse = 10 cm. Since sin 30° = opposite/10, opposite = 10 × 0.5 = 5 cm.
Example 2: find the adjacent side
If θ = 60° and the hypotenuse is 8 m, adjacent = 8 × cos 60° = 4 m. Verify the answer is shorter than the hypotenuse.
Example 3: find an angle
Opposite = 6 cm and adjacent = 8 cm. tan θ = 6/8 = 0.75. Therefore θ = tan⁻¹(0.75) ≈ 36.9°. Use degree mode, not radian mode, on your calculator.
Five mistakes students should avoid
- Using SOHCAHTOA for a triangle that is not right-angled.
- Labelling “opposite” without first choosing the reference angle.
- Using a calculator in radian mode when the question uses degrees.
- Rounding intermediate values too soon.
- Omitting units or failing to check whether the length is sensible.
A quick 15-minute practice plan
- Draw and label two right triangles.
- For each, identify the hypotenuse, opposite and adjacent.
- Solve one side-length and one angle question.
- Check with a different strategy or estimate.
- Explain why that trig ratio was selected.
For examination practice use past papers and mark schemes directory, or explore IGCSE Maths tutoring in Abu Dhabi for IGCSE-focused support.
Questions parents and students ask
Does SOHCAHTOA work on every triangle?
It directly applies to right-angled triangles. Other triangles may require the sine or cosine rule.
How do I know when to use tan?
Use tangent when the opposite and adjacent sides are the relevant pair.
Why does my calculator show a strange answer?
Check that it is in degree mode and that you used the inverse trigonometric function when finding an angle.