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Year 12 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 3 — 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 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 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
2.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 45°. Find the side opposite the 45° angle, to 1 decimal place.

Answer: 9.9 cm

  1. sin 45° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 45°
  3. ≈ 9.9
3.In a right-angled triangle, the hypotenuse is 5 cm and one angle is 24°. Find the side opposite the 24° angle, to 1 decimal place.

Answer: 2 cm

  1. sin 24° = opposite ÷ hypotenuse
  2. opposite = 5 × sin 24°
  3. ≈ 2
4.In a right-angled triangle, the hypotenuse is 6 cm and one angle is 55°. Find the side opposite the 55° angle, to 1 decimal place.

Answer: 4.9 cm

  1. sin 55° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 55°
  3. ≈ 4.9
5.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 26°. Find the side opposite the 26° angle, to 1 decimal place.

Answer: 9.6 cm

  1. sin 26° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 26°
  3. ≈ 9.6
6.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 51°. Find the side opposite the 51° angle, to 1 decimal place.

Answer: 12.4 cm

  1. sin 51° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 51°
  3. ≈ 12.4
7.In a right-angled triangle, the hypotenuse is 28 cm and one angle is 56°. Find the side opposite the 56° angle, to 1 decimal place.

Answer: 23.2 cm

  1. sin 56° = opposite ÷ hypotenuse
  2. opposite = 28 × sin 56°
  3. ≈ 23.2
8.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 67°. Find the side opposite the 67° angle, to 1 decimal place.

Answer: 17.5 cm

  1. sin 67° = opposite ÷ hypotenuse
  2. opposite = 19 × sin 67°
  3. ≈ 17.5
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