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Year 10 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 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 — Practice Set 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 67° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 37.7 m

  1. tan 67° = opposite ÷ adjacent
  2. opposite = 16 × tan 67°
  3. ≈ 37.7
2.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 33°. Find the side adjacent to the 33° angle, to 1 decimal place.

Answer: 6.7 cm

  1. cos 33° = adjacent ÷ hypotenuse
  2. adjacent = 8 × cos 33°
  3. ≈ 6.7
3.In a right-angled triangle, the hypotenuse is 28 cm and one angle is 57°. Find the side opposite the 57° angle, to 1 decimal place.

Answer: 23.5 cm

  1. sin 57° = opposite ÷ hypotenuse
  2. opposite = 28 × sin 57°
  3. ≈ 23.5
4.In a right-angled triangle, the hypotenuse is 30 cm and one angle is 24°. Find the side adjacent to the 24° angle, to 1 decimal place.

Answer: 27.4 cm

  1. cos 24° = adjacent ÷ hypotenuse
  2. adjacent = 30 × cos 24°
  3. ≈ 27.4
5.In a right-angled triangle, the side adjacent to a 38° angle is 22 m. Find the opposite side, to 1 decimal place.

Answer: 17.2 m

  1. tan 38° = opposite ÷ adjacent
  2. opposite = 22 × tan 38°
  3. ≈ 17.2
6.In a right-angled triangle, the hypotenuse is 6 cm and one angle is 44°. Find the side opposite the 44° angle, to 1 decimal place.

Answer: 4.2 cm

  1. sin 44° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 44°
  3. ≈ 4.2
7.In a right-angled triangle, the side adjacent to a 25° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 7.5 m

  1. tan 25° = opposite ÷ adjacent
  2. opposite = 16 × tan 25°
  3. ≈ 7.5
8.In a right-angled triangle, the hypotenuse is 25 cm and one angle is 49°. Find the side opposite the 49° angle, to 1 decimal place.

Answer: 18.9 cm

  1. sin 49° = opposite ÷ hypotenuse
  2. opposite = 25 × sin 49°
  3. ≈ 18.9
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