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Year 10 Trigonometry (Finding Sides) Worksheet — Level 2 — 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 2 — 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 33°. Find the side adjacent to the 33° angle, to 1 decimal place.

Answer: 4.2 cm

  1. cos 33° = adjacent ÷ hypotenuse
  2. adjacent = 5 × cos 33°
  3. ≈ 4.2
2.In a right-angled triangle, the hypotenuse is 28 cm and one angle is 22°. Find the side opposite the 22° angle, to 1 decimal place.

Answer: 10.5 cm

  1. sin 22° = opposite ÷ hypotenuse
  2. opposite = 28 × sin 22°
  3. ≈ 10.5
3.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
4.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 37°. Find the side opposite the 37° angle, to 1 decimal place.

Answer: 16.2 cm

  1. sin 37° = opposite ÷ hypotenuse
  2. opposite = 27 × sin 37°
  3. ≈ 16.2
5.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
6.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 29°. Find the side adjacent to the 29° angle, to 1 decimal place.

Answer: 13.1 cm

  1. cos 29° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 29°
  3. ≈ 13.1
7.In a right-angled triangle, the hypotenuse is 17 cm and one angle is 52°. Find the side adjacent to the 52° angle, to 1 decimal place.

Answer: 10.5 cm

  1. cos 52° = adjacent ÷ hypotenuse
  2. adjacent = 17 × cos 52°
  3. ≈ 10.5
8.In a right-angled triangle, the side adjacent to a 33° angle is 8 m. Find the opposite side, to 1 decimal place.

Answer: 5.2 m

  1. tan 33° = opposite ÷ adjacent
  2. opposite = 8 × tan 33°
  3. ≈ 5.2
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