SOH-CAH-TOA
Memory aid for the three basic ratios.
Key idea
Memory aid for the three basic ratios.
In depth
A mnemonic: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. To use it, name the sides relative to the angle, then pick the ratio that includes the two sides you care about.
Worked example
Hypotenuse 10, angle 30°, find the opposite side: sin 30° = x/10, so x = 5.
Real-world uses
- A quick memory aid for solving right-angled triangle problems in school and on site
Common mistake
Using the ratios in a triangle without a right angle.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is SOH-CAH-TOA?
Memory aid for the three basic ratios. It is a topic at the beginner level in Trigonometry.
Where is SOH-CAH-TOA used in real life?
Real-world examples: A quick memory aid for solving right-angled triangle problems in school and on site.
What should I learn before SOH-CAH-TOA?
Make sure you are comfortable with Tangent Ratio, the previous topic in Trigonometry.
What is a common mistake with SOH-CAH-TOA?
Using the ratios in a triangle without a right angle.
How can I practise SOH-CAH-TOA?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after SOH-CAH-TOA?
Move on to Reciprocal Trig Functions next.
Related beginner topics in Trigonometry
- Angle Measure: Degrees – A full turn is 360°; angles measure rotation.
- Right Triangle Terminology – Hypotenuse, opposite and adjacent sides relative to an angle.