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Year 11 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 4 — 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 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 6 cm and one angle is 35°. Find the side opposite the 35° angle, to 1 decimal place.

Answer: 3.4 cm

  1. sin 35° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 35°
  3. ≈ 3.4
2.In a right-angled triangle, the hypotenuse is 26 cm and one angle is 66°. Find the side opposite the 66° angle, to 1 decimal place.

Answer: 23.8 cm

  1. sin 66° = opposite ÷ hypotenuse
  2. opposite = 26 × sin 66°
  3. ≈ 23.8
3.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 37°. Find the side opposite the 37° angle, to 1 decimal place.

Answer: 9.6 cm

  1. sin 37° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 37°
  3. ≈ 9.6
4.In a right-angled triangle, the hypotenuse is 12 cm and one angle is 24°. Find the side opposite the 24° angle, to 1 decimal place.

Answer: 4.9 cm

  1. sin 24° = opposite ÷ hypotenuse
  2. opposite = 12 × sin 24°
  3. ≈ 4.9
5.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 38°. Find the side opposite the 38° angle, to 1 decimal place.

Answer: 6.8 cm

  1. sin 38° = opposite ÷ hypotenuse
  2. opposite = 11 × sin 38°
  3. ≈ 6.8
6.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 60°. Find the side opposite the 60° angle, to 1 decimal place.

Answer: 11.3 cm

  1. sin 60° = opposite ÷ hypotenuse
  2. opposite = 13 × sin 60°
  3. ≈ 11.3
7.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 68°. Find the side opposite the 68° angle, to 1 decimal place.

Answer: 25 cm

  1. sin 68° = opposite ÷ hypotenuse
  2. opposite = 27 × sin 68°
  3. ≈ 25
8.In a right-angled triangle, the hypotenuse is 25 cm and one angle is 65°. Find the side opposite the 65° angle, to 1 decimal place.

Answer: 22.7 cm

  1. sin 65° = opposite ÷ hypotenuse
  2. opposite = 25 × sin 65°
  3. ≈ 22.7
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