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Year 11 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

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

1.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 35°. Find the side adjacent to the 35° angle, to 1 decimal place.

Answer: 11.5 cm

  1. cos 35° = adjacent ÷ hypotenuse
  2. adjacent = 14 × cos 35°
  3. ≈ 11.5
2.In a right-angled triangle, the side adjacent to a 44° angle is 24 m. Find the opposite side, to 1 decimal place.

Answer: 23.2 m

  1. tan 44° = opposite ÷ adjacent
  2. opposite = 24 × tan 44°
  3. ≈ 23.2
3.In a right-angled triangle, the side adjacent to a 55° angle is 15 m. Find the opposite side, to 1 decimal place.

Answer: 21.4 m

  1. tan 55° = opposite ÷ adjacent
  2. opposite = 15 × tan 55°
  3. ≈ 21.4
4.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
5.In a right-angled triangle, the side adjacent to a 58° angle is 13 m. Find the opposite side, to 1 decimal place.

Answer: 20.8 m

  1. tan 58° = opposite ÷ adjacent
  2. opposite = 13 × tan 58°
  3. ≈ 20.8
6.In a right-angled triangle, the side adjacent to a 34° angle is 8 m. Find the opposite side, to 1 decimal place.

Answer: 5.4 m

  1. tan 34° = opposite ÷ adjacent
  2. opposite = 8 × tan 34°
  3. ≈ 5.4
7.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 41°. Find the side opposite the 41° angle, to 1 decimal place.

Answer: 13.1 cm

  1. sin 41° = opposite ÷ hypotenuse
  2. opposite = 20 × sin 41°
  3. ≈ 13.1
8.In a right-angled triangle, the side adjacent to a 47° angle is 6 m. Find the opposite side, to 1 decimal place.

Answer: 6.4 m

  1. tan 47° = opposite ÷ adjacent
  2. opposite = 6 × tan 47°
  3. ≈ 6.4
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