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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 side adjacent to a 39° angle is 6 m. Find the opposite side, to 1 decimal place.

Answer: 4.9 m

  1. tan 39° = opposite ÷ adjacent
  2. opposite = 6 × tan 39°
  3. ≈ 4.9
2.In a right-angled triangle, the hypotenuse is 18 cm and one angle is 57°. Find the side opposite the 57° angle, to 1 decimal place.

Answer: 15.1 cm

  1. sin 57° = opposite ÷ hypotenuse
  2. opposite = 18 × sin 57°
  3. ≈ 15.1
3.In a right-angled triangle, the side adjacent to a 31° angle is 15 m. Find the opposite side, to 1 decimal place.

Answer: 9 m

  1. tan 31° = opposite ÷ adjacent
  2. opposite = 15 × tan 31°
  3. ≈ 9
4.In a right-angled triangle, the side adjacent to a 32° angle is 6 m. Find the opposite side, to 1 decimal place.

Answer: 3.7 m

  1. tan 32° = opposite ÷ adjacent
  2. opposite = 6 × tan 32°
  3. ≈ 3.7
5.In a right-angled triangle, the side adjacent to a 22° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 4.4 m

  1. tan 22° = opposite ÷ adjacent
  2. opposite = 11 × tan 22°
  3. ≈ 4.4
6.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 24°. Find the side opposite the 24° angle, to 1 decimal place.

Answer: 8.1 cm

  1. sin 24° = opposite ÷ hypotenuse
  2. opposite = 20 × sin 24°
  3. ≈ 8.1
7.In a right-angled triangle, the side adjacent to a 57° angle is 4 m. Find the opposite side, to 1 decimal place.

Answer: 6.2 m

  1. tan 57° = opposite ÷ adjacent
  2. opposite = 4 × tan 57°
  3. ≈ 6.2
8.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 64°. Find the side opposite the 64° angle, to 1 decimal place.

Answer: 7.2 cm

  1. sin 64° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 64°
  3. ≈ 7.2
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