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

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

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Year 11 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 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 29 cm and one angle is 25°. Find the side opposite the 25° angle, to 1 decimal place.

Answer: 12.3 cm

  1. sin 25° = opposite ÷ hypotenuse
  2. opposite = 29 × sin 25°
  3. ≈ 12.3
2.In a right-angled triangle, the side adjacent to a 36° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 11.6 m

  1. tan 36° = opposite ÷ adjacent
  2. opposite = 16 × tan 36°
  3. ≈ 11.6
3.In a right-angled triangle, the hypotenuse is 24 cm and one angle is 53°. Find the side adjacent to the 53° angle, to 1 decimal place.

Answer: 14.4 cm

  1. cos 53° = adjacent ÷ hypotenuse
  2. adjacent = 24 × cos 53°
  3. ≈ 14.4
4.In a right-angled triangle, the hypotenuse is 23 cm and one angle is 65°. Find the side opposite the 65° angle, to 1 decimal place.

Answer: 20.8 cm

  1. sin 65° = opposite ÷ hypotenuse
  2. opposite = 23 × sin 65°
  3. ≈ 20.8
5.In a right-angled triangle, the side adjacent to a 34° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 6.1 m

  1. tan 34° = opposite ÷ adjacent
  2. opposite = 9 × tan 34°
  3. ≈ 6.1
6.In a right-angled triangle, the side adjacent to a 44° angle is 15 m. Find the opposite side, to 1 decimal place.

Answer: 14.5 m

  1. tan 44° = opposite ÷ adjacent
  2. opposite = 15 × tan 44°
  3. ≈ 14.5
7.In a right-angled triangle, the hypotenuse is 23 cm and one angle is 39°. Find the side opposite the 39° angle, to 1 decimal place.

Answer: 14.5 cm

  1. sin 39° = opposite ÷ hypotenuse
  2. opposite = 23 × sin 39°
  3. ≈ 14.5
8.In a right-angled triangle, the side adjacent to a 45° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 11 m

  1. tan 45° = opposite ÷ adjacent
  2. opposite = 11 × tan 45°
  3. ≈ 11
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