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Year 12 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 12 trigonometry worksheet.

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Trigonometry

Year 12 Trigonometry (Finding Sides) Worksheet — Level 2 — 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 24° angle is 14 m. Find the opposite side, to 1 decimal place.

Answer: 6.2 m

  1. tan 24° = opposite ÷ adjacent
  2. opposite = 14 × tan 24°
  3. ≈ 6.2
2.In a right-angled triangle, the side adjacent to a 52° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 14.1 m

  1. tan 52° = opposite ÷ adjacent
  2. opposite = 11 × tan 52°
  3. ≈ 14.1
3.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 58°. Find the side opposite the 58° angle, to 1 decimal place.

Answer: 6.8 cm

  1. sin 58° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 58°
  3. ≈ 6.8
4.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 26°. Find the side adjacent to the 26° angle, to 1 decimal place.

Answer: 19.8 cm

  1. cos 26° = adjacent ÷ hypotenuse
  2. adjacent = 22 × cos 26°
  3. ≈ 19.8
5.In a right-angled triangle, the side adjacent to a 37° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 14.3 m

  1. tan 37° = opposite ÷ adjacent
  2. opposite = 19 × tan 37°
  3. ≈ 14.3
6.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 53°. Find the side adjacent to the 53° angle, to 1 decimal place.

Answer: 16.2 cm

  1. cos 53° = adjacent ÷ hypotenuse
  2. adjacent = 27 × cos 53°
  3. ≈ 16.2
7.In a right-angled triangle, the side adjacent to a 68° angle is 17 m. Find the opposite side, to 1 decimal place.

Answer: 42.1 m

  1. tan 68° = opposite ÷ adjacent
  2. opposite = 17 × tan 68°
  3. ≈ 42.1
8.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 35°. Find the side opposite the 35° angle, to 1 decimal place.

Answer: 10.9 cm

  1. sin 35° = opposite ÷ hypotenuse
  2. opposite = 19 × sin 35°
  3. ≈ 10.9
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