Trigonometry Basics: SOH CAH TOA Without the Panic
May 9, 2026 · 5 min · trigonometry basics · SOH CAH TOA · trig help
Trigonometry boils down to three ratios in a right-angled triangle. Once you know which side is which, the rest is bookkeeping.
Naming the sides
- Hypotenuse — the longest side, opposite the right angle
- Opposite — the side facing the angle you're working with
- Adjacent — the side next to that angle (not the hypotenuse)
Pick one angle in the triangle and label the other two sides relative to it. The hypotenuse never moves.
The three ratios
- sin = opposite / hypotenuse
- cos = adjacent / hypotenuse
- tan = opposite / adjacent
That's the whole "SOH CAH TOA" rhyme. Memorise it once, write it on every exam paper before you start.
When to use which
Look at the question. Identify which two sides you have or want.
- Have hypotenuse + want opposite → use sin
- Have hypotenuse + want adjacent → use cos
- Have opposite + want adjacent (or vice versa) → use tan
That's it. The rest is calculator work.
Worked example
Right triangle. The angle is 30°. The hypotenuse is 10. Find the opposite side.
- sin(30) = opposite / 10
- 0.5 = opposite / 10
- opposite = 5
When SOH CAH TOA stops working
Only on right-angled triangles. For non-right triangles, use the sine rule or cosine rule.
- Sine rule: a / sin A = b / sin B = c / sin C
- Cosine rule: c² = a² + b² - 2ab cos C
You'll use these in IGCSE Year 11, A Level, IB, AP, and any first-year engineering course.