Success TutoringWorksheets

Year 11 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 11 trigonometry worksheet.

Download answers PDFPrint answersBack to worksheet

Year 11 · Mathematics · Trigonometry

Year 11 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

Success Tutoring

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

1.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 42°. Find the side opposite the 42° angle, to 1 decimal place.

Answer: 10.7 cm

  1. sin 42° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 42°
  3. ≈ 10.7
2.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 62°. Find the side opposite the 62° angle, to 1 decimal place.

Answer: 15.9 cm

  1. sin 62° = opposite ÷ hypotenuse
  2. opposite = 18 × sin 62°
  3. ≈ 15.9
3.In a right-angled triangle, the side adjacent to a 22° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 6.5 m

  1. tan 22° = opposite ÷ adjacent
  2. opposite = 16 × tan 22°
  3. ≈ 6.5
4.In a right-angled triangle, the side adjacent to a 29° angle is 18 m. Find the opposite side, to 1 decimal place.

Answer: 10 m

  1. tan 29° = opposite ÷ adjacent
  2. opposite = 18 × tan 29°
  3. ≈ 10
5.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 35°. Find the side adjacent to the 35° angle, to 1 decimal place.

Answer: 11.5 cm

  1. cos 35° = adjacent ÷ hypotenuse
  2. adjacent = 14 × cos 35°
  3. ≈ 11.5
6.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 63°. Find the side adjacent to the 63° angle, to 1 decimal place.

Answer: 10 cm

  1. cos 63° = adjacent ÷ hypotenuse
  2. adjacent = 22 × cos 63°
  3. ≈ 10
7.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 29°. Find the side adjacent to the 29° angle, to 1 decimal place.

Answer: 9.6 cm

  1. cos 29° = adjacent ÷ hypotenuse
  2. adjacent = 11 × cos 29°
  3. ≈ 9.6
8.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 56°. Find the side opposite the 56° angle, to 1 decimal place.

Answer: 9.1 cm

  1. sin 56° = opposite ÷ hypotenuse
  2. opposite = 11 × sin 56°
  3. ≈ 9.1
worksheets.successtutoring.com · Free to print and share 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.