Trigonometry Question Generator
Right-angled trigonometry, where the whole difficulty is choosing the ratio before doing any arithmetic. Each question names which two sides are involved relative to the angle — opposite and hypotenuse, adjacent and hypotenuse, or opposite and adjacent — because the sides are named relative to the angle and not to the page. Inverse questions, where the angle is the unknown, appear above the gentle level.
What this generator does
Produces questions with an angle and one side given, asking for another side, or with two sides given, asking for the angle. Answers are to two decimal places for sides and one for angles, which is the convention most syllabuses use.
How to use this tool
- Choose the number of questions and the level.
- Identify the two sides in play, then pick sine, cosine or tangent.
- Reveal the answers to check, or the working to see the ratio named.
- Seed the set so a group can work through the identical questions.
Understanding the controls
- How many questions
- Between 1 and 20. Ten is a normal set once inverse questions are mixed in.
- Level
- Gentle uses sine and cosine only, with the angle always given. Standard adds tangent and inverse questions, and stretch widens the sides and the angle range.
- Seed
- Reproduces the same triangles and angles from a word you choose.
- Show the answers / working
- The missing side or angle, or the ratio selection and the substitution behind it.
Common use cases
- Drilling the choice of ratio rather than the calculator work
- Mixing find-a-side and find-an-angle questions in one set
- Practice with tangent, which only appears once the hypotenuse is not involved
- Reinforcing that sides are named relative to the angle, not the diagram
- Handing out the same set of questions from a seed
How this generator works
An angle and a side are drawn, and the missing side is that side times the appropriate ratio. Inverse questions draw an opposite and a hypotenuse with the opposite strictly shorter, so the arcsine is always defined. The check recomputes the answer from the given values and requires it to match after rounding, and rejects any inverse question where the opposite side reaches the hypotenuse.
Randomness and fairness
The angle, the side and which ratio is exercised are random; the arithmetic is not. Seeded sets reproduce exactly and are therefore explicitly not cryptographically secure. Without a seed the browser's cryptographically secure generator supplies the draws.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Right-angled triangles only. The sine and cosine rules for other triangles are not covered.
- Angles are in degrees throughout — radians are never used.
- Inverse questions always use sine, so arccos and arctan are not exercised as separate types.
- No diagram is drawn; the triangle is described in words.
- Question sets are not saved between visits.
Privacy and your data
Angles and sides are drawn locally and the arithmetic runs in your browser. Nothing is transmitted or retained.
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