Success TutoringWorksheets

Year 12 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 12 trigonometry worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Trigonometry

Year 12 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 4 — Answers

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

1.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 67°. Find the side opposite the 67° angle, to 1 decimal place.

Answer: 19.3 cm

  1. sin 67° = opposite ÷ hypotenuse
  2. opposite = 21 × sin 67°
  3. ≈ 19.3
2.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 21°. Find the side adjacent to the 21° angle, to 1 decimal place.

Answer: 20.5 cm

  1. cos 21° = adjacent ÷ hypotenuse
  2. adjacent = 22 × cos 21°
  3. ≈ 20.5
3.In a right-angled triangle, the hypotenuse is 23 cm and one angle is 26°. Find the side opposite the 26° angle, to 1 decimal place.

Answer: 10.1 cm

  1. sin 26° = opposite ÷ hypotenuse
  2. opposite = 23 × sin 26°
  3. ≈ 10.1
4.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 44°. Find the side adjacent to the 44° angle, to 1 decimal place.

Answer: 7.9 cm

  1. cos 44° = adjacent ÷ hypotenuse
  2. adjacent = 11 × cos 44°
  3. ≈ 7.9
5.In a right-angled triangle, the hypotenuse is 24 cm and one angle is 68°. Find the side adjacent to the 68° angle, to 1 decimal place.

Answer: 9 cm

  1. cos 68° = adjacent ÷ hypotenuse
  2. adjacent = 24 × cos 68°
  3. ≈ 9
6.In a right-angled triangle, the side adjacent to a 45° angle is 23 m. Find the opposite side, to 1 decimal place.

Answer: 23 m

  1. tan 45° = opposite ÷ adjacent
  2. opposite = 23 × tan 45°
  3. ≈ 23
7.In a right-angled triangle, the side adjacent to a 32° angle is 4 m. Find the opposite side, to 1 decimal place.

Answer: 2.5 m

  1. tan 32° = opposite ÷ adjacent
  2. opposite = 4 × tan 32°
  3. ≈ 2.5
8.In a right-angled triangle, the side adjacent to a 57° angle is 22 m. Find the opposite side, to 1 decimal place.

Answer: 33.9 m

  1. tan 57° = opposite ÷ adjacent
  2. opposite = 22 × tan 57°
  3. ≈ 33.9
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: