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Year 10 Trigonometry (Finding Sides) Worksheet — Level 3 — 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 3 — 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 side adjacent to a 43° angle is 8 m. Find the opposite side, to 1 decimal place.

Answer: 7.5 m

  1. tan 43° = opposite ÷ adjacent
  2. opposite = 8 × tan 43°
  3. ≈ 7.5
2.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 54°. Find the side adjacent to the 54° angle, to 1 decimal place.

Answer: 12.3 cm

  1. cos 54° = adjacent ÷ hypotenuse
  2. adjacent = 21 × cos 54°
  3. ≈ 12.3
3.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 45°. Find the side adjacent to the 45° angle, to 1 decimal place.

Answer: 14.1 cm

  1. cos 45° = adjacent ÷ hypotenuse
  2. adjacent = 20 × cos 45°
  3. ≈ 14.1
4.In a right-angled triangle, the side adjacent to a 34° angle is 5 m. Find the opposite side, to 1 decimal place.

Answer: 3.4 m

  1. tan 34° = opposite ÷ adjacent
  2. opposite = 5 × tan 34°
  3. ≈ 3.4
5.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 57°. Find the side adjacent to the 57° angle, to 1 decimal place.

Answer: 12 cm

  1. cos 57° = adjacent ÷ hypotenuse
  2. adjacent = 22 × cos 57°
  3. ≈ 12
6.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 32°. Find the side adjacent to the 32° angle, to 1 decimal place.

Answer: 8.5 cm

  1. cos 32° = adjacent ÷ hypotenuse
  2. adjacent = 10 × cos 32°
  3. ≈ 8.5
7.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 37°. Find the side adjacent to the 37° angle, to 1 decimal place.

Answer: 5.6 cm

  1. cos 37° = adjacent ÷ hypotenuse
  2. adjacent = 7 × cos 37°
  3. ≈ 5.6
8.In a right-angled triangle, the side adjacent to a 70° angle is 18 m. Find the opposite side, to 1 decimal place.

Answer: 49.5 m

  1. tan 70° = opposite ÷ adjacent
  2. opposite = 18 × tan 70°
  3. ≈ 49.5
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