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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 hypotenuse is 15 cm and one angle is 43°. Find the side adjacent to the 43° angle, to 1 decimal place.

Answer: 11 cm

  1. cos 43° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 43°
  3. ≈ 11
2.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 41°. Find the side opposite the 41° angle, to 1 decimal place.

Answer: 5.9 cm

  1. sin 41° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 41°
  3. ≈ 5.9
3.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 60°. Find the side opposite the 60° angle, to 1 decimal place.

Answer: 11.3 cm

  1. sin 60° = opposite ÷ hypotenuse
  2. opposite = 13 × sin 60°
  3. ≈ 11.3
4.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 21°. Find the side adjacent to the 21° angle, to 1 decimal place.

Answer: 20.5 cm

  1. cos 21° = adjacent ÷ hypotenuse
  2. adjacent = 22 × cos 21°
  3. ≈ 20.5
5.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 37°. Find the side adjacent to the 37° angle, to 1 decimal place.

Answer: 16 cm

  1. cos 37° = adjacent ÷ hypotenuse
  2. adjacent = 20 × cos 37°
  3. ≈ 16
6.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 45°. Find the side adjacent to the 45° angle, to 1 decimal place.

Answer: 13.4 cm

  1. cos 45° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 45°
  3. ≈ 13.4
7.In a right-angled triangle, the side adjacent to a 57° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 16.9 m

  1. tan 57° = opposite ÷ adjacent
  2. opposite = 11 × tan 57°
  3. ≈ 16.9
8.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 59°. Find the side opposite the 59° angle, to 1 decimal place.

Answer: 6.9 cm

  1. sin 59° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 59°
  3. ≈ 6.9
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