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Year 12 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 12 trigonometry worksheet.

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Year 12 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 4 — Answers

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

1.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 64°. Find the side opposite the 64° angle, to 1 decimal place.

Answer: 26.1 cm

  1. sin 64° = opposite ÷ hypotenuse
  2. opposite = 29 × sin 64°
  3. ≈ 26.1
2.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 69°. Find the side opposite the 69° angle, to 1 decimal place.

Answer: 20.5 cm

  1. sin 69° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 69°
  3. ≈ 20.5
3.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 49°. Find the side opposite the 49° angle, to 1 decimal place.

Answer: 8.3 cm

  1. sin 49° = opposite ÷ hypotenuse
  2. opposite = 11 × sin 49°
  3. ≈ 8.3
4.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 10.9 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 43°
  3. ≈ 10.9
5.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 46°. Find the side opposite the 46° angle, to 1 decimal place.

Answer: 10.1 cm

  1. sin 46° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 46°
  3. ≈ 10.1
6.In a right-angled triangle, the hypotenuse is 6 cm and one angle is 67°. Find the side opposite the 67° angle, to 1 decimal place.

Answer: 5.5 cm

  1. sin 67° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 67°
  3. ≈ 5.5
7.In a right-angled triangle, the hypotenuse is 30 cm and one angle is 66°. Find the side opposite the 66° angle, to 1 decimal place.

Answer: 27.4 cm

  1. sin 66° = opposite ÷ hypotenuse
  2. opposite = 30 × sin 66°
  3. ≈ 27.4
8.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 35°. Find the side opposite the 35° angle, to 1 decimal place.

Answer: 5.7 cm

  1. sin 35° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 35°
  3. ≈ 5.7
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