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Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 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 — Practice Set 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 23 cm and one angle is 26°. Find the side adjacent to the 26° angle, to 1 decimal place.

Answer: 20.7 cm

  1. cos 26° = adjacent ÷ hypotenuse
  2. adjacent = 23 × cos 26°
  3. ≈ 20.7
2.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 61°. Find the side opposite the 61° angle, to 1 decimal place.

Answer: 17.5 cm

  1. sin 61° = opposite ÷ hypotenuse
  2. opposite = 20 × sin 61°
  3. ≈ 17.5
3.In a right-angled triangle, the side adjacent to a 21° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 6.1 m

  1. tan 21° = opposite ÷ adjacent
  2. opposite = 16 × tan 21°
  3. ≈ 6.1
4.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 39°. Find the side opposite the 39° angle, to 1 decimal place.

Answer: 5 cm

  1. sin 39° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 39°
  3. ≈ 5
5.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 47°. Find the side adjacent to the 47° angle, to 1 decimal place.

Answer: 13 cm

  1. cos 47° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 47°
  3. ≈ 13
6.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 23°. Find the side opposite the 23° angle, to 1 decimal place.

Answer: 10.5 cm

  1. sin 23° = opposite ÷ hypotenuse
  2. opposite = 27 × sin 23°
  3. ≈ 10.5
7.In a right-angled triangle, the side adjacent to a 69° angle is 22 m. Find the opposite side, to 1 decimal place.

Answer: 57.3 m

  1. tan 69° = opposite ÷ adjacent
  2. opposite = 22 × tan 69°
  3. ≈ 57.3
8.In a right-angled triangle, the side adjacent to a 27° angle is 14 m. Find the opposite side, to 1 decimal place.

Answer: 7.1 m

  1. tan 27° = opposite ÷ adjacent
  2. opposite = 14 × tan 27°
  3. ≈ 7.1
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