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Year 10 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 3 — 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 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 69°. Find the side adjacent to the 69° angle, to 1 decimal place.

Answer: 5.7 cm

  1. cos 69° = adjacent ÷ hypotenuse
  2. adjacent = 16 × cos 69°
  3. ≈ 5.7
2.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 40°. Find the side adjacent to the 40° angle, to 1 decimal place.

Answer: 7.7 cm

  1. cos 40° = adjacent ÷ hypotenuse
  2. adjacent = 10 × cos 40°
  3. ≈ 7.7
3.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 60°. Find the side adjacent to the 60° angle, to 1 decimal place.

Answer: 9.5 cm

  1. cos 60° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 60°
  3. ≈ 9.5
4.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 41°. Find the side opposite the 41° angle, to 1 decimal place.

Answer: 5.9 cm

  1. sin 41° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 41°
  3. ≈ 5.9
5.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 68°. Find the side adjacent to the 68° angle, to 1 decimal place.

Answer: 10.9 cm

  1. cos 68° = adjacent ÷ hypotenuse
  2. adjacent = 29 × cos 68°
  3. ≈ 10.9
6.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 38°. Find the side adjacent to the 38° angle, to 1 decimal place.

Answer: 11.8 cm

  1. cos 38° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 38°
  3. ≈ 11.8
7.In a right-angled triangle, the hypotenuse is 17 cm and one angle is 64°. Find the side adjacent to the 64° angle, to 1 decimal place.

Answer: 7.5 cm

  1. cos 64° = adjacent ÷ hypotenuse
  2. adjacent = 17 × cos 64°
  3. ≈ 7.5
8.In a right-angled triangle, the side adjacent to a 24° angle is 6 m. Find the opposite side, to 1 decimal place.

Answer: 2.7 m

  1. tan 24° = opposite ÷ adjacent
  2. opposite = 6 × tan 24°
  3. ≈ 2.7
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