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Year 10 Trigonometry (Finding Sides) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 10 trigonometry worksheet.

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Trigonometry

Year 10 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 19 cm and one angle is 21°. Find the side adjacent to the 21° angle, to 1 decimal place.

Answer: 17.7 cm

  1. cos 21° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 21°
  3. ≈ 17.7
2.In a right-angled triangle, the side adjacent to a 69° angle is 4 m. Find the opposite side, to 1 decimal place.

Answer: 10.4 m

  1. tan 69° = opposite ÷ adjacent
  2. opposite = 4 × tan 69°
  3. ≈ 10.4
3.In a right-angled triangle, the side adjacent to a 43° angle is 15 m. Find the opposite side, to 1 decimal place.

Answer: 14 m

  1. tan 43° = opposite ÷ adjacent
  2. opposite = 15 × tan 43°
  3. ≈ 14
4.In a right-angled triangle, the hypotenuse is 24 cm and one angle is 61°. Find the side adjacent to the 61° angle, to 1 decimal place.

Answer: 11.6 cm

  1. cos 61° = adjacent ÷ hypotenuse
  2. adjacent = 24 × cos 61°
  3. ≈ 11.6
5.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 33°. Find the side opposite the 33° angle, to 1 decimal place.

Answer: 3.8 cm

  1. sin 33° = opposite ÷ hypotenuse
  2. opposite = 7 × sin 33°
  3. ≈ 3.8
6.In a right-angled triangle, the side adjacent to a 68° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 47 m

  1. tan 68° = opposite ÷ adjacent
  2. opposite = 19 × tan 68°
  3. ≈ 47
7.In a right-angled triangle, the hypotenuse is 28 cm and one angle is 33°. Find the side opposite the 33° angle, to 1 decimal place.

Answer: 15.2 cm

  1. sin 33° = opposite ÷ hypotenuse
  2. opposite = 28 × sin 33°
  3. ≈ 15.2
8.In a right-angled triangle, the hypotenuse is 17 cm and one angle is 38°. Find the side adjacent to the 38° angle, to 1 decimal place.

Answer: 13.4 cm

  1. cos 38° = adjacent ÷ hypotenuse
  2. adjacent = 17 × cos 38°
  3. ≈ 13.4
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