Success TutoringWorksheets

Year 9 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 9 trigonometry worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Trigonometry

Year 9 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

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

1.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 57°. Find the side adjacent to the 57° angle, to 1 decimal place.

Answer: 10.9 cm

  1. cos 57° = adjacent ÷ hypotenuse
  2. adjacent = 20 × cos 57°
  3. ≈ 10.9
2.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 36°. Find the side opposite the 36° angle, to 1 decimal place.

Answer: 12.9 cm

  1. sin 36° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 36°
  3. ≈ 12.9
3.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 63°. Find the side adjacent to the 63° angle, to 1 decimal place.

Answer: 12.3 cm

  1. cos 63° = adjacent ÷ hypotenuse
  2. adjacent = 27 × cos 63°
  3. ≈ 12.3
4.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 37°. Find the side opposite the 37° angle, to 1 decimal place.

Answer: 13.2 cm

  1. sin 37° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 37°
  3. ≈ 13.2
5.In a right-angled triangle, the side adjacent to a 45° angle is 7 m. Find the opposite side, to 1 decimal place.

Answer: 7 m

  1. tan 45° = opposite ÷ adjacent
  2. opposite = 7 × tan 45°
  3. ≈ 7
6.In a right-angled triangle, the side adjacent to a 31° angle is 4 m. Find the opposite side, to 1 decimal place.

Answer: 2.4 m

  1. tan 31° = opposite ÷ adjacent
  2. opposite = 4 × tan 31°
  3. ≈ 2.4
7.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 50°. Find the side adjacent to the 50° angle, to 1 decimal place.

Answer: 13.5 cm

  1. cos 50° = adjacent ÷ hypotenuse
  2. adjacent = 21 × cos 50°
  3. ≈ 13.5
8.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 70°. Find the side opposite the 70° angle, to 1 decimal place.

Answer: 7.5 cm

  1. sin 70° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 70°
  3. ≈ 7.5
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.