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Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 11 trigonometry worksheet.

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Year 11 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 hypotenuse is 10 cm and one angle is 34°. Find the side adjacent to the 34° angle, to 1 decimal place.

Answer: 8.3 cm

  1. cos 34° = adjacent ÷ hypotenuse
  2. adjacent = 10 × cos 34°
  3. ≈ 8.3
2.In a right-angled triangle, the hypotenuse is 6 cm and one angle is 30°. Find the side adjacent to the 30° angle, to 1 decimal place.

Answer: 5.2 cm

  1. cos 30° = adjacent ÷ hypotenuse
  2. adjacent = 6 × cos 30°
  3. ≈ 5.2
3.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 65°. Find the side opposite the 65° angle, to 1 decimal place.

Answer: 18.1 cm

  1. sin 65° = opposite ÷ hypotenuse
  2. opposite = 20 × sin 65°
  3. ≈ 18.1
4.In a right-angled triangle, the side adjacent to a 59° angle is 24 m. Find the opposite side, to 1 decimal place.

Answer: 39.9 m

  1. tan 59° = opposite ÷ adjacent
  2. opposite = 24 × tan 59°
  3. ≈ 39.9
5.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 63°. Find the side adjacent to the 63° angle, to 1 decimal place.

Answer: 7.3 cm

  1. cos 63° = adjacent ÷ hypotenuse
  2. adjacent = 16 × cos 63°
  3. ≈ 7.3
6.In a right-angled triangle, the hypotenuse is 23 cm and one angle is 28°. Find the side adjacent to the 28° angle, to 1 decimal place.

Answer: 20.3 cm

  1. cos 28° = adjacent ÷ hypotenuse
  2. adjacent = 23 × cos 28°
  3. ≈ 20.3
7.In a right-angled triangle, the side adjacent to a 25° angle is 12 m. Find the opposite side, to 1 decimal place.

Answer: 5.6 m

  1. tan 25° = opposite ÷ adjacent
  2. opposite = 12 × tan 25°
  3. ≈ 5.6
8.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 70°. Find the side opposite the 70° angle, to 1 decimal place.

Answer: 13.2 cm

  1. sin 70° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 70°
  3. ≈ 13.2
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