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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 15 cm and one angle is 30°. Find the side opposite the 30° angle, to 1 decimal place.

Answer: 7.5 cm

  1. sin 30° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 30°
  3. ≈ 7.5
2.In a right-angled triangle, the side adjacent to a 42° angle is 23 m. Find the opposite side, to 1 decimal place.

Answer: 20.7 m

  1. tan 42° = opposite ÷ adjacent
  2. opposite = 23 × tan 42°
  3. ≈ 20.7
3.In a right-angled triangle, the hypotenuse is 7 cm and one angle is 52°. Find the side adjacent to the 52° angle, to 1 decimal place.

Answer: 4.3 cm

  1. cos 52° = adjacent ÷ hypotenuse
  2. adjacent = 7 × cos 52°
  3. ≈ 4.3
4.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 48°. Find the side adjacent to the 48° angle, to 1 decimal place.

Answer: 7.4 cm

  1. cos 48° = adjacent ÷ hypotenuse
  2. adjacent = 11 × cos 48°
  3. ≈ 7.4
5.In a right-angled triangle, the side adjacent to a 55° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 15.7 m

  1. tan 55° = opposite ÷ adjacent
  2. opposite = 11 × tan 55°
  3. ≈ 15.7
6.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 40°. Find the side opposite the 40° angle, to 1 decimal place.

Answer: 9.6 cm

  1. sin 40° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 40°
  3. ≈ 9.6
7.In a right-angled triangle, the side adjacent to a 50° angle is 18 m. Find the opposite side, to 1 decimal place.

Answer: 21.5 m

  1. tan 50° = opposite ÷ adjacent
  2. opposite = 18 × tan 50°
  3. ≈ 21.5
8.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 64°. Find the side opposite the 64° angle, to 1 decimal place.

Answer: 17.1 cm

  1. sin 64° = opposite ÷ hypotenuse
  2. opposite = 19 × sin 64°
  3. ≈ 17.1
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