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Year 9 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 9 trigonometry worksheet.

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Year 9 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 5 cm and one angle is 24°. Find the side adjacent to the 24° angle, to 1 decimal place.

Answer: 4.6 cm

  1. cos 24° = adjacent ÷ hypotenuse
  2. adjacent = 5 × cos 24°
  3. ≈ 4.6
2.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 33°. Find the side adjacent to the 33° angle, to 1 decimal place.

Answer: 6.7 cm

  1. cos 33° = adjacent ÷ hypotenuse
  2. adjacent = 8 × cos 33°
  3. ≈ 6.7
3.In a right-angled triangle, the side adjacent to a 49° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 12.7 m

  1. tan 49° = opposite ÷ adjacent
  2. opposite = 11 × tan 49°
  3. ≈ 12.7
4.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 41°. Find the side adjacent to the 41° angle, to 1 decimal place.

Answer: 6 cm

  1. cos 41° = adjacent ÷ hypotenuse
  2. adjacent = 8 × cos 41°
  3. ≈ 6
5.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 53°. Find the side adjacent to the 53° angle, to 1 decimal place.

Answer: 11.4 cm

  1. cos 53° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 53°
  3. ≈ 11.4
6.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 64°. Find the side opposite the 64° angle, to 1 decimal place.

Answer: 14.4 cm

  1. sin 64° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 64°
  3. ≈ 14.4
7.In a right-angled triangle, the side adjacent to a 20° angle is 13 m. Find the opposite side, to 1 decimal place.

Answer: 4.7 m

  1. tan 20° = opposite ÷ adjacent
  2. opposite = 13 × tan 20°
  3. ≈ 4.7
8.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 64°. Find the side opposite the 64° angle, to 1 decimal place.

Answer: 13.5 cm

  1. sin 64° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 64°
  3. ≈ 13.5
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