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Year 10 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 4 — 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 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 5 cm and one angle is 68°. Find the side opposite the 68° angle, to 1 decimal place.

Answer: 4.6 cm

  1. sin 68° = opposite ÷ hypotenuse
  2. opposite = 5 × sin 68°
  3. ≈ 4.6
2.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 63°. Find the side opposite the 63° angle, to 1 decimal place.

Answer: 17.8 cm

  1. sin 63° = opposite ÷ hypotenuse
  2. opposite = 20 × sin 63°
  3. ≈ 17.8
3.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 67°. Find the side opposite the 67° angle, to 1 decimal place.

Answer: 12 cm

  1. sin 67° = opposite ÷ hypotenuse
  2. opposite = 13 × sin 67°
  3. ≈ 12
4.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 41°. Find the side opposite the 41° angle, to 1 decimal place.

Answer: 10.5 cm

  1. sin 41° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 41°
  3. ≈ 10.5
5.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 44°. Find the side opposite the 44° angle, to 1 decimal place.

Answer: 11.1 cm

  1. sin 44° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 44°
  3. ≈ 11.1
6.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 21°. Find the side opposite the 21° angle, to 1 decimal place.

Answer: 3.6 cm

  1. sin 21° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 21°
  3. ≈ 3.6
7.In a right-angled triangle, the hypotenuse is 25 cm and one angle is 30°. Find the side opposite the 30° angle, to 1 decimal place.

Answer: 12.5 cm

  1. sin 30° = opposite ÷ hypotenuse
  2. opposite = 25 × sin 30°
  3. ≈ 12.5
8.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 21°. Find the side opposite the 21° angle, to 1 decimal place.

Answer: 2.5 cm

  1. sin 21° = opposite ÷ hypotenuse
  2. opposite = 7 × sin 21°
  3. ≈ 2.5
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