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Year 11 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 3 — 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 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 8 cm and one angle is 62°. Find the side opposite the 62° angle, to 1 decimal place.

Answer: 7.1 cm

  1. sin 62° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 62°
  3. ≈ 7.1
2.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 20°. Find the side opposite the 20° angle, to 1 decimal place.

Answer: 4.8 cm

  1. sin 20° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 20°
  3. ≈ 4.8
3.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 63°. Find the side opposite the 63° angle, to 1 decimal place.

Answer: 16.9 cm

  1. sin 63° = opposite ÷ hypotenuse
  2. opposite = 19 × sin 63°
  3. ≈ 16.9
4.In a right-angled triangle, the hypotenuse is 12 cm and one angle is 60°. Find the side opposite the 60° angle, to 1 decimal place.

Answer: 10.4 cm

  1. sin 60° = opposite ÷ hypotenuse
  2. opposite = 12 × sin 60°
  3. ≈ 10.4
5.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 34°. Find the side opposite the 34° angle, to 1 decimal place.

Answer: 5 cm

  1. sin 34° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 34°
  3. ≈ 5
6.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 23°. Find the side opposite the 23° angle, to 1 decimal place.

Answer: 3.9 cm

  1. sin 23° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 23°
  3. ≈ 3.9
7.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
8.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 4.8 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 7 × sin 43°
  3. ≈ 4.8
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