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Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 4 — Answers

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

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Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 4 — 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 64° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 18.5 m

  1. tan 64° = opposite ÷ adjacent
  2. opposite = 9 × tan 64°
  3. ≈ 18.5
2.In a right-angled triangle, the side adjacent to a 55° angle is 24 m. Find the opposite side, to 1 decimal place.

Answer: 34.3 m

  1. tan 55° = opposite ÷ adjacent
  2. opposite = 24 × tan 55°
  3. ≈ 34.3
3.In a right-angled triangle, the hypotenuse is 23 cm and one angle is 52°. Find the side adjacent to the 52° angle, to 1 decimal place.

Answer: 14.2 cm

  1. cos 52° = adjacent ÷ hypotenuse
  2. adjacent = 23 × cos 52°
  3. ≈ 14.2
4.In a right-angled triangle, the side adjacent to a 61° angle is 15 m. Find the opposite side, to 1 decimal place.

Answer: 27.1 m

  1. tan 61° = opposite ÷ adjacent
  2. opposite = 15 × tan 61°
  3. ≈ 27.1
5.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 6.1 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 43°
  3. ≈ 6.1
6.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 26°. Find the side adjacent to the 26° angle, to 1 decimal place.

Answer: 6.3 cm

  1. cos 26° = adjacent ÷ hypotenuse
  2. adjacent = 7 × cos 26°
  3. ≈ 6.3
7.In a right-angled triangle, the side adjacent to a 67° angle is 10 m. Find the opposite side, to 1 decimal place.

Answer: 23.6 m

  1. tan 67° = opposite ÷ adjacent
  2. opposite = 10 × tan 67°
  3. ≈ 23.6
8.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 27°. Find the side adjacent to the 27° angle, to 1 decimal place.

Answer: 8 cm

  1. cos 27° = adjacent ÷ hypotenuse
  2. adjacent = 9 × cos 27°
  3. ≈ 8
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