Study Guide
Trigonometric Functions, Radians and Exact Values
A senior study guide to radian measure, the exact-value table, the unit circle (ASTC) and the basic trigonometric graphs. Worked examples…
- Difficulty
- Level 3 · Challenge
- Time
- 30 min
WorksheetYear 12Level 1 · Easier
Free Year 12 Trigonometry (Finding Sides) Worksheet — Level 1
Use sine, cosine and tangent to find unknown sides in right-angled triangles. Builds confidence with the core skill before adding complexity. This Year 12 worksheet has 8 questions and comes with a full answer sheet showing the working for every question.
Need more practice? Practice Set 2 · Practice Set 3 · Practice Set 4 — same skill, fresh questions, full answers.
Instant download · No sign-up · Free for personal, classroom and homeschool use
- Year
- Year 12
- Subject
- Maths
- Topic
- Trigonometry
- Difficulty
- Level 1 · Easier
- Estimated time
- 20 minutes
- Curriculum
- New Zealand Curriculum
- Questions
- 8
- Answers
- Included, with working
- Format
- PDF (A4), print or complete online
Students will practise
- labelling sides relative to an angle
- choosing the correct trigonometric ratio
- finding unknown sides
Curriculum: New Zealand Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
What's next?
Completed: Year 12 Trigonometry (Finding Sides) Worksheet — Level 1
How to use this worksheet
- Print the PDF or complete it on screen. Write the student's name and date at the top.
- Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
- Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
- Record the score, celebrate what went well, then follow the "What's next" suggestion.
Common questions
Who is this worksheet for?
Year 12 students (typically ages 16–17) working on trigonometry. It is pitched at level 1 · easier; a harder version is linked above.
Are the answers included?
Yes. The PDF includes a full answer sheet with the working for every question. You can also view the answers online.
How long does it take?
About 20 minutes for 8 questions. Short, regular sessions work best: two or three a week beats one long one.
Do I need to sign up to download?
No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.
What should we do next?
Try Year 12 Trigonometry (Finding Sides) Worksheet — Level 2.
Preview
Success TutoringWorksheetsYear 12 · Mathematics · TrigonometryYear 12 Trigonometry (Finding Sides) Worksheet — Level 1
Name
Date
Score /
Label the sides (opposite, adjacent, hypotenuse), choose the ratio (SOH CAH TOA), then solve.
1.In a right-angled triangle, the hypotenuse is 12 cm and one angle is 66°. Find the side opposite the 66° angle, to 1 decimal place.
2.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 25°. Find the side opposite the 25° angle, to 1 decimal place.
3.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 39°. Find the side opposite the 39° angle, to 1 decimal place.
4.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 22°. Find the side opposite the 22° angle, to 1 decimal place.
5.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 57°. Find the side opposite the 57° angle, to 1 decimal place.
6.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 38°. Find the side opposite the 38° angle, to 1 decimal place.
7.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 36°. Find the side opposite the 36° angle, to 1 decimal place.
8.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 23°. Find the side opposite the 23° angle, to 1 decimal place.
Preview — the PDF contains the full resource and answer sheet.
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Year 12 Trigonometry (Finding Sides) Worksheet — Level 2
Use sine, cosine and tangent to find unknown sides in right-angled triangles. Expected-level practice for this year group. This Year 12…
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- Time
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- Questions
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- Answers
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- Worksheet
Year 12 Trigonometry (Finding Sides) Worksheet — Level 3
Use sine, cosine and tangent to find unknown sides in right-angled triangles. A challenge set for students ready to stretch further. This…
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Trigonometry in other year levels
- Year 11 Trigonometry (Finding Sides) Worksheet — Level 1
Worksheet · Year 11 · Trigonometry · Level 1 · Easier
- Year 11 Trigonometry (Finding Sides) Worksheet — Level 2
Worksheet · Year 11 · Trigonometry · Level 2 · Standard
- Year 10 Trigonometry (Finding Sides) Worksheet — Level 1
Worksheet · Year 10 · Trigonometry · Level 1 · Easier
- Year 10 Trigonometry (Finding Sides) Worksheet — Level 2
Worksheet · Year 10 · Trigonometry · Level 2 · Standard
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About this resource
- Created by
- Success Tutoring Maths Team
- Reviewed by
- Success Tutoring
- Last reviewed
- 1 October 2026
- How it was made
- Generated by checked procedures
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