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

Label the sides (opposite, adjacent, hypotenuse), choose the ratio (SOH CAH TOA), then solve.

1.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 65°. Find the side adjacent to the 65° angle, to 1 decimal place.

Answer: 5.5 cm

  1. cos 65° = adjacent ÷ hypotenuse
  2. adjacent = 13 × cos 65°
  3. ≈ 5.5
2.In a right-angled triangle, the side adjacent to a 53° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 25.2 m

  1. tan 53° = opposite ÷ adjacent
  2. opposite = 19 × tan 53°
  3. ≈ 25.2
3.In a right-angled triangle, the hypotenuse is 26 cm and one angle is 42°. Find the side adjacent to the 42° angle, to 1 decimal place.

Answer: 19.3 cm

  1. cos 42° = adjacent ÷ hypotenuse
  2. adjacent = 26 × cos 42°
  3. ≈ 19.3
4.In a right-angled triangle, the side adjacent to a 36° angle is 4 m. Find the opposite side, to 1 decimal place.

Answer: 2.9 m

  1. tan 36° = opposite ÷ adjacent
  2. opposite = 4 × tan 36°
  3. ≈ 2.9
5.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 30°. Find the side adjacent to the 30° angle, to 1 decimal place.

Answer: 12.1 cm

  1. cos 30° = adjacent ÷ hypotenuse
  2. adjacent = 14 × cos 30°
  3. ≈ 12.1
6.In a right-angled triangle, the side adjacent to a 23° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 4.7 m

  1. tan 23° = opposite ÷ adjacent
  2. opposite = 11 × tan 23°
  3. ≈ 4.7
7.In a right-angled triangle, the side adjacent to a 61° angle is 13 m. Find the opposite side, to 1 decimal place.

Answer: 23.5 m

  1. tan 61° = opposite ÷ adjacent
  2. opposite = 13 × tan 61°
  3. ≈ 23.5
8.In a right-angled triangle, the side adjacent to a 64° angle is 21 m. Find the opposite side, to 1 decimal place.

Answer: 43.1 m

  1. tan 64° = opposite ÷ adjacent
  2. opposite = 21 × tan 64°
  3. ≈ 43.1
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