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Year 11 Trigonometry (Finding Sides) Worksheet — Level 1 — Practice Set 3 — 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 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 16 cm and one angle is 63°. Find the side opposite the 63° angle, to 1 decimal place.

Answer: 14.3 cm

  1. sin 63° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 63°
  3. ≈ 14.3
2.In a right-angled triangle, the hypotenuse is 30 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 20.5 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 30 × sin 43°
  3. ≈ 20.5
3.In a right-angled triangle, the hypotenuse is 5 cm and one angle is 45°. Find the side opposite the 45° angle, to 1 decimal place.

Answer: 3.5 cm

  1. sin 45° = opposite ÷ hypotenuse
  2. opposite = 5 × sin 45°
  3. ≈ 3.5
4.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 56°. Find the side opposite the 56° angle, to 1 decimal place.

Answer: 12.4 cm

  1. sin 56° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 56°
  3. ≈ 12.4
5.In a right-angled triangle, the hypotenuse is 25 cm and one angle is 54°. Find the side opposite the 54° angle, to 1 decimal place.

Answer: 20.2 cm

  1. sin 54° = opposite ÷ hypotenuse
  2. opposite = 25 × sin 54°
  3. ≈ 20.2
6.In a right-angled triangle, the hypotenuse is 5 cm and one angle is 21°. Find the side opposite the 21° angle, to 1 decimal place.

Answer: 1.8 cm

  1. sin 21° = opposite ÷ hypotenuse
  2. opposite = 5 × sin 21°
  3. ≈ 1.8
7.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 58°. Find the side opposite the 58° angle, to 1 decimal place.

Answer: 6.8 cm

  1. sin 58° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 58°
  3. ≈ 6.8
8.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 58°. Find the side opposite the 58° angle, to 1 decimal place.

Answer: 11.9 cm

  1. sin 58° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 58°
  3. ≈ 11.9
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