SOH-CAH-TOA
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Label sides
Identify opposite, adjacent, hypotenuse - Find a side using sin
Use sin to find a missing side - Find a side using cos/tan
Use cos or tan to find a missing side - Find an angle
Use inverse trig to find angles - Real-world trig
Apply trig to elevation and depression
Before This Topic
Your child should be comfortable with:
- Pythagoras' Theorem (Year 8)
- Angles (Year 5)
Common Mistakes
- Labelling the sides incorrectly — confusing adjacent and opposite (especially when the triangle is rotated)
The hypotenuse is always the longest side, opposite the right angle. The opposite side is across from the angle you are working with. The adjacent side is next to the angle you are working with (and is NOT the hypotenuse). Rotate the page if it helps. - Using the wrong ratio (e.g. using sin when they should use tan) because they have not identified which sides they have
Write SOH-CAH-TOA and label your triangle first. If you have the Opposite and Hypotenuse, use Sin. If you have the Adjacent and Hypotenuse, use Cos. If you have the Opposite and Adjacent, use Tan. Identify the sides BEFORE choosing the formula.
Tips for Parents
- Help your child memorise SOH-CAH-TOA with a mnemonic: "Some Old Houses Can Always Hide Their Old Age" or make up your own. The important thing is knowing which ratio uses which sides.
- Practise labelling triangles: draw a right-angled triangle, mark one of the other angles, and ask your child to label O (opposite), A (adjacent), and H (hypotenuse). Do this several times with the angle in different positions.
- Make sure your child's calculator is set to DEGREES mode, not radians. This is a very common source of wrong answers — the button might say "DEG" or "D".
- Use real examples: "A tree casts a shadow 10 metres long. The angle from the tip of the shadow to the top of the tree is 35°. How tall is the tree?" Use tan(35) = height/10.
Key Words
- SOH-CAH-TOA — A memory aid for the three trig ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
- Hypotenuse — The longest side of a right-angled triangle, always opposite the right angle.
- Opposite — The side across from the angle you are working with — it does not touch that angle.
- Adjacent — The side next to the angle you are working with (not the hypotenuse) — it touches that angle.
- Inverse trig (sin⁻¹, cos⁻¹, tan⁻¹) — The reverse operation used to find an angle when you know two sides — e.g. if sin(x) = 0.5, then x = sin⁻¹(0.5) = 30°.
Where This Fits
Before this topic: Children should be confident with Pythagoras' Theorem, understand right-angled triangles, and be able to use a calculator for square roots.
After this topic: Basic trigonometry leads to the sine and cosine rules for non-right-angled triangles, trig graphs, trig identities, and radians at A-level.
How MathCraft Teaches This
In MathCraft, SOH-CAH-TOA is taught through the Geometry & Shape adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise SOH-CAH-TOA with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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