SOH CAH TOA might sound like a foreign language, but it is genuinely just three simple ratios — and once the pattern clicks, your child will wonder what the fuss was about.
What Your Child Is Learning
Trigonometry is about finding missing sides and angles in right-angled triangles. Your child uses three ratios — sine, cosine, and tangent — to connect angles to side lengths.
Every right-angled triangle has three sides with special names, depending on which angle you are working with:
Hypotenuse — always the longest side, opposite the right angle.
Opposite — the side directly opposite the angle you are looking at.
Adjacent — the side next to the angle (that is not the hypotenuse).
This is the most important thing to understand: the hypotenuse never changes — it's always opposite the right angle. But opposite and adjacent swap depending on which angle you're working with.
Looking from angle A
Looking from angle B
Same triangle. Same sides. Different angle.
The hypotenuse (red) stays the same — it's always the longest side, always opposite the right angle.
But the opposite and adjacent swap depending on which angle you're working from. This is the single most common mistake in trigonometry.
The three ratios connect these sides to the angle:
The mnemonic SOH CAH TOA is still the standard way to remember the three ratios:
SOH
Sin = Opp / Hyp
CAH
Cos = Adj / Hyp
TOA
Tan = Opp / Adj
The method your child follows is always the same three steps:
Label the sides — identify which is opposite, adjacent, and hypotenuse relative to the angle in the question.
Choose the right ratio — look at which two sides are involved (one known, one unknown) and pick SOH, CAH, or TOA accordingly.
Rearrange and solve — substitute the values in and use a calculator.
Parent tip
You do not need to remember any trigonometry yourself. The most helpful thing you can do is check that your child has labelled the sides correctly before they start calculating. If the labels are right, the rest usually follows.
Common Mistakes to Watch For
Classic mistake
Mixing up opposite and adjacent. Which side is "opposite" and which is "adjacent" depends on which angle you are working with. If your child picks a different angle, the labels swap. This is the number one source of wrong answers in trig questions.
Calculator trap
Calculator in the wrong mode. At GCSE, angles are always in degrees. If the calculator is set to radians, every answer will be wrong. On most scientific calculators, look for a small "D" or "DEG" on the display. If it says "R" or "RAD", it needs changing.
Watch out
Using the wrong trig function. Students sometimes just pick sin because it is the first one they learned. The choice of sin, cos, or tan must match which sides they are working with. If the question involves the opposite and hypotenuse, it is sin. If it involves adjacent and hypotenuse, it is cos. Opposite and adjacent? Tan.
Try It Together
Here is a worked example:
A right-angled triangle has an angle of 30 degrees and a hypotenuse of 10 cm. Find the length of the side opposite the 30-degree angle.
We know the angle (30 degrees) and the hypotenuse (10 cm). We want the opposite side.
Opposite and hypotenuse → that is SOH: \(\sin(\theta) = \frac{\text{Opp}}{\text{Hyp}}\)
Substitute: \(\sin(30°) = \frac{\text{Opp}}{10}\)
We know \(\sin(30°) = 0.5\), so: \(0.5 = \frac{\text{Opp}}{10}\)
Multiply both sides by 10: \(\text{Opp} = 10 \times 0.5 = 5 \text{ cm}\)
Ask your child: "If you are standing 20 metres from a building and you look up at 45 degrees to see the top, how tall is the building?" (Hint: \(\tan(45°) = 1\), so the building is 20 metres tall.) Trigonometry is just measuring things you cannot reach directly.
Let Them Practise
Trigonometry is one of those topics where practice makes a real difference. Once the labelling becomes automatic, students can tackle these questions quickly and confidently.
We have two free games that make trig practice genuinely engaging: