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Year 9 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 9 trigonometry worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Trigonometry

Year 9 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 24 cm and one angle is 70°. Find the side opposite the 70° angle, to 1 decimal place.

Answer: 22.6 cm

  1. sin 70° = opposite ÷ hypotenuse
  2. opposite = 24 × sin 70°
  3. ≈ 22.6
2.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 40°. Find the side opposite the 40° angle, to 1 decimal place.

Answer: 14.1 cm

  1. sin 40° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 40°
  3. ≈ 14.1
3.In a right-angled triangle, the side adjacent to a 41° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 7.8 m

  1. tan 41° = opposite ÷ adjacent
  2. opposite = 9 × tan 41°
  3. ≈ 7.8
4.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 47°. Find the side opposite the 47° angle, to 1 decimal place.

Answer: 15.4 cm

  1. sin 47° = opposite ÷ hypotenuse
  2. opposite = 21 × sin 47°
  3. ≈ 15.4
5.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 26°. Find the side opposite the 26° angle, to 1 decimal place.

Answer: 12.7 cm

  1. sin 26° = opposite ÷ hypotenuse
  2. opposite = 29 × sin 26°
  3. ≈ 12.7
6.In a right-angled triangle, the side adjacent to a 61° angle is 7 m. Find the opposite side, to 1 decimal place.

Answer: 12.6 m

  1. tan 61° = opposite ÷ adjacent
  2. opposite = 7 × tan 61°
  3. ≈ 12.6
7.In a right-angled triangle, the side adjacent to a 66° angle is 25 m. Find the opposite side, to 1 decimal place.

Answer: 56.2 m

  1. tan 66° = opposite ÷ adjacent
  2. opposite = 25 × tan 66°
  3. ≈ 56.2
8.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 33°. Find the side adjacent to the 33° angle, to 1 decimal place.

Answer: 12.6 cm

  1. cos 33° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 33°
  3. ≈ 12.6
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