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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 6 cm and one angle is 62°. Find the side opposite the 62° angle, to 1 decimal place.

Answer: 5.3 cm

  1. sin 62° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 62°
  3. ≈ 5.3
2.In a right-angled triangle, the hypotenuse is 28 cm and one angle is 40°. Find the side opposite the 40° angle, to 1 decimal place.

Answer: 18 cm

  1. sin 40° = opposite ÷ hypotenuse
  2. opposite = 28 × sin 40°
  3. ≈ 18
3.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 33°. Find the side opposite the 33° angle, to 1 decimal place.

Answer: 9.8 cm

  1. sin 33° = opposite ÷ hypotenuse
  2. opposite = 18 × sin 33°
  3. ≈ 9.8
4.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 40°. Find the side opposite the 40° angle, to 1 decimal place.

Answer: 5.8 cm

  1. sin 40° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 40°
  3. ≈ 5.8
5.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 40°. Find the side opposite the 40° angle, to 1 decimal place.

Answer: 8.4 cm

  1. sin 40° = opposite ÷ hypotenuse
  2. opposite = 13 × sin 40°
  3. ≈ 8.4
6.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 24°. Find the side opposite the 24° angle, to 1 decimal place.

Answer: 6.1 cm

  1. sin 24° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 24°
  3. ≈ 6.1
7.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 19.8 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 29 × sin 43°
  3. ≈ 19.8
8.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 37°. Find the side opposite the 37° angle, to 1 decimal place.

Answer: 10.8 cm

  1. sin 37° = opposite ÷ hypotenuse
  2. opposite = 18 × sin 37°
  3. ≈ 10.8
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