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Year 11 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 11 trigonometry worksheet.

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Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Trigonometry

Year 11 Trigonometry (Finding Sides) Worksheet — Level 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 5 cm and one angle is 43°. Find the side adjacent to the 43° angle, to 1 decimal place.

Answer: 3.7 cm

  1. cos 43° = adjacent ÷ hypotenuse
  2. adjacent = 5 × cos 43°
  3. ≈ 3.7
2.In a right-angled triangle, the side adjacent to a 38° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 14.8 m

  1. tan 38° = opposite ÷ adjacent
  2. opposite = 19 × tan 38°
  3. ≈ 14.8
3.In a right-angled triangle, the side adjacent to a 38° angle is 17 m. Find the opposite side, to 1 decimal place.

Answer: 13.3 m

  1. tan 38° = opposite ÷ adjacent
  2. opposite = 17 × tan 38°
  3. ≈ 13.3
4.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 41°. Find the side adjacent to the 41° angle, to 1 decimal place.

Answer: 11.3 cm

  1. cos 41° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 41°
  3. ≈ 11.3
5.In a right-angled triangle, the side adjacent to a 68° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 47 m

  1. tan 68° = opposite ÷ adjacent
  2. opposite = 19 × tan 68°
  3. ≈ 47
6.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 36°. Find the side adjacent to the 36° angle, to 1 decimal place.

Answer: 8.9 cm

  1. cos 36° = adjacent ÷ hypotenuse
  2. adjacent = 11 × cos 36°
  3. ≈ 8.9
7.In a right-angled triangle, the side adjacent to a 23° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 8.1 m

  1. tan 23° = opposite ÷ adjacent
  2. opposite = 19 × tan 23°
  3. ≈ 8.1
8.In a right-angled triangle, the side adjacent to a 32° angle is 10 m. Find the opposite side, to 1 decimal place.

Answer: 6.2 m

  1. tan 32° = opposite ÷ adjacent
  2. opposite = 10 × tan 32°
  3. ≈ 6.2
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