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Year 11 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 2 — Answers

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

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Year 11 Trigonometry (Finding Sides) Worksheet — Level 1 — 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 27 cm and one angle is 70°. Find the side opposite the 70° angle, to 1 decimal place.

Answer: 25.4 cm

  1. sin 70° = opposite ÷ hypotenuse
  2. opposite = 27 × sin 70°
  3. ≈ 25.4
2.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 41°. Find the side opposite the 41° angle, to 1 decimal place.

Answer: 6.6 cm

  1. sin 41° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 41°
  3. ≈ 6.6
3.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 67°. Find the side opposite the 67° angle, to 1 decimal place.

Answer: 10.1 cm

  1. sin 67° = opposite ÷ hypotenuse
  2. opposite = 11 × sin 67°
  3. ≈ 10.1
4.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 67°. Find the side opposite the 67° angle, to 1 decimal place.

Answer: 16.6 cm

  1. sin 67° = opposite ÷ hypotenuse
  2. opposite = 18 × sin 67°
  3. ≈ 16.6
5.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 27°. Find the side opposite the 27° angle, to 1 decimal place.

Answer: 4.1 cm

  1. sin 27° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 27°
  3. ≈ 4.1
6.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 59°. Find the side opposite the 59° angle, to 1 decimal place.

Answer: 12.9 cm

  1. sin 59° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 59°
  3. ≈ 12.9
7.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 54°. Find the side opposite the 54° angle, to 1 decimal place.

Answer: 11.3 cm

  1. sin 54° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 54°
  3. ≈ 11.3
8.In a right-angled triangle, the hypotenuse is 6 cm and one angle is 34°. Find the side opposite the 34° angle, to 1 decimal place.

Answer: 3.4 cm

  1. sin 34° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 34°
  3. ≈ 3.4
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