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WorksheetYear 10Level 3 · Challenge

Free Year 10 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 Year 10 worksheet has 8 questions and comes with a full answer sheet showing the working for every question.

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Year
Year 10
Subject
Mathematics
Topic
Trigonometry
Difficulty
Level 3 · Challenge
Estimated time
20 minutes
Curriculum
Australian Curriculum
Questions
8
Answers
Included, with working
Format
PDF (A4) + print

Students will practise

  • labelling sides relative to an angle
  • choosing the correct trigonometric ratio
  • finding unknown sides

Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Year 10 Trigonometry (Finding Sides) Worksheet — Level 3

Ready for more? Move on to Year 11 Mathematics.

How to use this worksheet

  1. Print the PDF or complete it on screen. Write the student's name and date at the top.
  2. Read the instructions for each part together before starting. Encourage working to be shown, not just answers.
  3. Mark with the answer sheet. Compare the method, not only the final answer, and give credit for correct working.
  4. Record the score, celebrate what went well, then follow the "What's next" suggestion.

Common questions

Who is this worksheet for?

Year 10 students (typically ages 15–16) working on trigonometry. It is pitched at level 3 · challenge; an easier 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?

Explore more Year 10 mathematics resources.

Preview

Year 10 · Mathematics · Trigonometry

Year 10 Trigonometry (Finding Sides) Worksheet — Level 3

Success Tutoring

Student name:

Date:

Score: /

Label the sides (opposite, adjacent, hypotenuse), choose the ratio (SOH CAH TOA), then solve.

1.In a right-angled triangle, the side adjacent to a 43° angle is 8 m. Find the opposite side, to 1 decimal place.
2.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 54°. Find the side adjacent to the 54° angle, to 1 decimal place.
3.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 45°. Find the side adjacent to the 45° angle, to 1 decimal place.
4.In a right-angled triangle, the side adjacent to a 34° angle is 5 m. Find the opposite side, to 1 decimal place.
5.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 57°. Find the side adjacent to the 57° angle, to 1 decimal place.
6.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 32°. Find the side adjacent to the 32° angle, to 1 decimal place.
7.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 37°. Find the side adjacent to the 37° angle, to 1 decimal place.
8.In a right-angled triangle, the side adjacent to a 70° angle is 18 m. Find the opposite side, to 1 decimal place.
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Preview — the PDF contains the full resource and answer sheet.

  • Worksheet

    Year 10 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 10…

    Difficulty
    Level 2 · Standard
    Time
    20 min
    Questions
    8 questions
    Answers
    Answers included

Trigonometry in other year levels

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

Free to print and share for personal, classroom and homeschool use. Please don't resell. Spotted an error? Let us know.