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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 7 cm and one angle is 26°. Find the side opposite the 26° angle, to 1 decimal place.

Answer: 3.1 cm

  1. sin 26° = opposite ÷ hypotenuse
  2. opposite = 7 × sin 26°
  3. ≈ 3.1
2.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 39°. Find the side opposite the 39° angle, to 1 decimal place.

Answer: 12 cm

  1. sin 39° = opposite ÷ hypotenuse
  2. opposite = 19 × sin 39°
  3. ≈ 12
3.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 28°. Find the side opposite the 28° angle, to 1 decimal place.

Answer: 8.5 cm

  1. sin 28° = opposite ÷ hypotenuse
  2. opposite = 18 × sin 28°
  3. ≈ 8.5
4.In a right-angled triangle, the hypotenuse is 26 cm and one angle is 24°. Find the side opposite the 24° angle, to 1 decimal place.

Answer: 10.6 cm

  1. sin 24° = opposite ÷ hypotenuse
  2. opposite = 26 × sin 24°
  3. ≈ 10.6
5.In a right-angled triangle, the hypotenuse is 5 cm and one angle is 27°. Find the side opposite the 27° angle, to 1 decimal place.

Answer: 2.3 cm

  1. sin 27° = opposite ÷ hypotenuse
  2. opposite = 5 × sin 27°
  3. ≈ 2.3
6.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 34°. Find the side opposite the 34° angle, to 1 decimal place.

Answer: 4.5 cm

  1. sin 34° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 34°
  3. ≈ 4.5
7.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 37°. Find the side opposite the 37° angle, to 1 decimal place.

Answer: 8.4 cm

  1. sin 37° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 37°
  3. ≈ 8.4
8.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 70°. Find the side opposite the 70° angle, to 1 decimal place.

Answer: 27.3 cm

  1. sin 70° = opposite ÷ hypotenuse
  2. opposite = 29 × sin 70°
  3. ≈ 27.3
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