Success TutoringWorksheets

Year 10 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 2 — Answers

Answer sheet with worked solutions for the Year 10 trigonometry worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Trigonometry

Year 10 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 2 — 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 25°. Find the side opposite the 25° angle, to 1 decimal place.

Answer: 8.9 cm

  1. sin 25° = opposite ÷ hypotenuse
  2. opposite = 21 × sin 25°
  3. ≈ 8.9
2.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 66°. Find the side adjacent to the 66° angle, to 1 decimal place.

Answer: 2.8 cm

  1. cos 66° = adjacent ÷ hypotenuse
  2. adjacent = 7 × cos 66°
  3. ≈ 2.8
3.In a right-angled triangle, the hypotenuse is 25 cm and one angle is 50°. Find the side adjacent to the 50° angle, to 1 decimal place.

Answer: 16.1 cm

  1. cos 50° = adjacent ÷ hypotenuse
  2. adjacent = 25 × cos 50°
  3. ≈ 16.1
4.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 24°. Find the side opposite the 24° angle, to 1 decimal place.

Answer: 7.3 cm

  1. sin 24° = opposite ÷ hypotenuse
  2. opposite = 18 × sin 24°
  3. ≈ 7.3
5.In a right-angled triangle, the side adjacent to a 31° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 5.4 m

  1. tan 31° = opposite ÷ adjacent
  2. opposite = 9 × tan 31°
  3. ≈ 5.4
6.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 29°. Find the side adjacent to the 29° angle, to 1 decimal place.

Answer: 23.6 cm

  1. cos 29° = adjacent ÷ hypotenuse
  2. adjacent = 27 × cos 29°
  3. ≈ 23.6
7.In a right-angled triangle, the side adjacent to a 54° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 26.2 m

  1. tan 54° = opposite ÷ adjacent
  2. opposite = 19 × tan 54°
  3. ≈ 26.2
8.In a right-angled triangle, the side adjacent to a 59° angle is 23 m. Find the opposite side, to 1 decimal place.

Answer: 38.3 m

  1. tan 59° = opposite ÷ adjacent
  2. opposite = 23 × tan 59°
  3. ≈ 38.3
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.