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Year 12 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 12 trigonometry worksheet.

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Year 12 · Mathematics · Trigonometry

Year 12 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 29° angle is 25 m. Find the opposite side, to 1 decimal place.

Answer: 13.9 m

  1. tan 29° = opposite ÷ adjacent
  2. opposite = 25 × tan 29°
  3. ≈ 13.9
2.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 30°. Find the side adjacent to the 30° angle, to 1 decimal place.

Answer: 15.6 cm

  1. cos 30° = adjacent ÷ hypotenuse
  2. adjacent = 18 × cos 30°
  3. ≈ 15.6
3.In a right-angled triangle, the hypotenuse is 24 cm and one angle is 43°. Find the side adjacent to the 43° angle, to 1 decimal place.

Answer: 17.6 cm

  1. cos 43° = adjacent ÷ hypotenuse
  2. adjacent = 24 × cos 43°
  3. ≈ 17.6
4.In a right-angled triangle, the side adjacent to a 60° angle is 23 m. Find the opposite side, to 1 decimal place.

Answer: 39.8 m

  1. tan 60° = opposite ÷ adjacent
  2. opposite = 23 × tan 60°
  3. ≈ 39.8
5.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 49°. Find the side adjacent to the 49° angle, to 1 decimal place.

Answer: 9.8 cm

  1. cos 49° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 49°
  3. ≈ 9.8
6.In a right-angled triangle, the side adjacent to a 39° angle is 14 m. Find the opposite side, to 1 decimal place.

Answer: 11.3 m

  1. tan 39° = opposite ÷ adjacent
  2. opposite = 14 × tan 39°
  3. ≈ 11.3
7.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 37°. Find the side adjacent to the 37° angle, to 1 decimal place.

Answer: 10.4 cm

  1. cos 37° = adjacent ÷ hypotenuse
  2. adjacent = 13 × cos 37°
  3. ≈ 10.4
8.In a right-angled triangle, the side adjacent to a 28° angle is 13 m. Find the opposite side, to 1 decimal place.

Answer: 6.9 m

  1. tan 28° = opposite ÷ adjacent
  2. opposite = 13 × tan 28°
  3. ≈ 6.9
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