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Year 10 Trigonometry (Finding Sides) Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the Year 10 trigonometry worksheet.

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Year 10 · Mathematics · Trigonometry

Year 10 Trigonometry (Finding Sides) Worksheet — Level 2 — Answers

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Label the sides (opposite, adjacent, hypotenuse), choose the ratio (SOH CAH TOA), then solve.

1.In a right-angled triangle, the hypotenuse is 23 cm and one angle is 26°. Find the side adjacent to the 26° angle, to 1 decimal place.

Answer: 20.7 cm

  1. cos 26° = adjacent ÷ hypotenuse
  2. adjacent = 23 × cos 26°
  3. ≈ 20.7
2.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 61°. Find the side adjacent to the 61° angle, to 1 decimal place.

Answer: 14.1 cm

  1. cos 61° = adjacent ÷ hypotenuse
  2. adjacent = 29 × cos 61°
  3. ≈ 14.1
3.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 28°. Find the side adjacent to the 28° angle, to 1 decimal place.

Answer: 16.8 cm

  1. cos 28° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 28°
  3. ≈ 16.8
4.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 57°. Find the side opposite the 57° angle, to 1 decimal place.

Answer: 18.5 cm

  1. sin 57° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 57°
  3. ≈ 18.5
5.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 52°. Find the side adjacent to the 52° angle, to 1 decimal place.

Answer: 12.9 cm

  1. cos 52° = adjacent ÷ hypotenuse
  2. adjacent = 21 × cos 52°
  3. ≈ 12.9
6.In a right-angled triangle, the side adjacent to a 69° angle is 13 m. Find the opposite side, to 1 decimal place.

Answer: 33.9 m

  1. tan 69° = opposite ÷ adjacent
  2. opposite = 13 × tan 69°
  3. ≈ 33.9
7.In a right-angled triangle, the side adjacent to a 70° angle is 20 m. Find the opposite side, to 1 decimal place.

Answer: 54.9 m

  1. tan 70° = opposite ÷ adjacent
  2. opposite = 20 × tan 70°
  3. ≈ 54.9
8.In a right-angled triangle, the hypotenuse is 28 cm and one angle is 30°. Find the side opposite the 30° angle, to 1 decimal place.

Answer: 14 cm

  1. sin 30° = opposite ÷ hypotenuse
  2. opposite = 28 × sin 30°
  3. ≈ 14
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