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Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — 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 2 — 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 16 cm and one angle is 42°. Find the side adjacent to the 42° angle, to 1 decimal place.

Answer: 11.9 cm

  1. cos 42° = adjacent ÷ hypotenuse
  2. adjacent = 16 × cos 42°
  3. ≈ 11.9
2.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 49°. Find the side adjacent to the 49° angle, to 1 decimal place.

Answer: 12.5 cm

  1. cos 49° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 49°
  3. ≈ 12.5
3.In a right-angled triangle, the hypotenuse is 25 cm and one angle is 69°. Find the side opposite the 69° angle, to 1 decimal place.

Answer: 23.3 cm

  1. sin 69° = opposite ÷ hypotenuse
  2. opposite = 25 × sin 69°
  3. ≈ 23.3
4.In a right-angled triangle, the side adjacent to a 48° angle is 23 m. Find the opposite side, to 1 decimal place.

Answer: 25.5 m

  1. tan 48° = opposite ÷ adjacent
  2. opposite = 23 × tan 48°
  3. ≈ 25.5
5.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 30°. Find the side opposite the 30° angle, to 1 decimal place.

Answer: 13.5 cm

  1. sin 30° = opposite ÷ hypotenuse
  2. opposite = 27 × sin 30°
  3. ≈ 13.5
6.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 27°. Find the side opposite the 27° angle, to 1 decimal place.

Answer: 12.3 cm

  1. sin 27° = opposite ÷ hypotenuse
  2. opposite = 27 × sin 27°
  3. ≈ 12.3
7.In a right-angled triangle, the side adjacent to a 35° angle is 18 m. Find the opposite side, to 1 decimal place.

Answer: 12.6 m

  1. tan 35° = opposite ÷ adjacent
  2. opposite = 18 × tan 35°
  3. ≈ 12.6
8.In a right-angled triangle, the hypotenuse is 12 cm and one angle is 50°. Find the side opposite the 50° angle, to 1 decimal place.

Answer: 9.2 cm

  1. sin 50° = opposite ÷ hypotenuse
  2. opposite = 12 × sin 50°
  3. ≈ 9.2
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