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Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — 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 2 — Answers

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 36° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 8 m

  1. tan 36° = opposite ÷ adjacent
  2. opposite = 11 × tan 36°
  3. ≈ 8
2.In a right-angled triangle, the side adjacent to a 53° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 21.2 m

  1. tan 53° = opposite ÷ adjacent
  2. opposite = 16 × tan 53°
  3. ≈ 21.2
3.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
4.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 24°. Find the side adjacent to the 24° angle, to 1 decimal place.

Answer: 24.7 cm

  1. cos 24° = adjacent ÷ hypotenuse
  2. adjacent = 27 × cos 24°
  3. ≈ 24.7
5.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 33°. Find the side opposite the 33° angle, to 1 decimal place.

Answer: 5.4 cm

  1. sin 33° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 33°
  3. ≈ 5.4
6.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 44°. Find the side opposite the 44° angle, to 1 decimal place.

Answer: 11.1 cm

  1. sin 44° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 44°
  3. ≈ 11.1
7.In a right-angled triangle, the side adjacent to a 55° angle is 14 m. Find the opposite side, to 1 decimal place.

Answer: 20 m

  1. tan 55° = opposite ÷ adjacent
  2. opposite = 14 × tan 55°
  3. ≈ 20
8.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
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