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Year 10 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 10 trigonometry worksheet.

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Year 10 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 5 cm and one angle is 36°. Find the side opposite the 36° angle, to 1 decimal place.

Answer: 2.9 cm

  1. sin 36° = opposite ÷ hypotenuse
  2. opposite = 5 × sin 36°
  3. ≈ 2.9
2.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 55°. Find the side opposite the 55° angle, to 1 decimal place.

Answer: 18 cm

  1. sin 55° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 55°
  3. ≈ 18
3.In a right-angled triangle, the hypotenuse is 12 cm and one angle is 23°. Find the side opposite the 23° angle, to 1 decimal place.

Answer: 4.7 cm

  1. sin 23° = opposite ÷ hypotenuse
  2. opposite = 12 × sin 23°
  3. ≈ 4.7
4.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 55°. Find the side opposite the 55° angle, to 1 decimal place.

Answer: 13.1 cm

  1. sin 55° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 55°
  3. ≈ 13.1
5.In a right-angled triangle, the hypotenuse is 6 cm and one angle is 61°. Find the side opposite the 61° angle, to 1 decimal place.

Answer: 5.2 cm

  1. sin 61° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 61°
  3. ≈ 5.2
6.In a right-angled triangle, the hypotenuse is 26 cm and one angle is 47°. Find the side opposite the 47° angle, to 1 decimal place.

Answer: 19 cm

  1. sin 47° = opposite ÷ hypotenuse
  2. opposite = 26 × sin 47°
  3. ≈ 19
7.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 28°. Find the side opposite the 28° angle, to 1 decimal place.

Answer: 13.6 cm

  1. sin 28° = opposite ÷ hypotenuse
  2. opposite = 29 × sin 28°
  3. ≈ 13.6
8.In a right-angled triangle, the hypotenuse is 17 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 11.6 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 17 × sin 43°
  3. ≈ 11.6
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