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Year 9 Trigonometry (Finding Sides) Worksheet — Level 3 — 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 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 6 cm and one angle is 65°. Find the side opposite the 65° angle, to 1 decimal place.

Answer: 5.4 cm

  1. sin 65° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 65°
  3. ≈ 5.4
2.In a right-angled triangle, the side adjacent to a 20° angle is 4 m. Find the opposite side, to 1 decimal place.

Answer: 1.5 m

  1. tan 20° = opposite ÷ adjacent
  2. opposite = 4 × tan 20°
  3. ≈ 1.5
3.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 52°. Find the side opposite the 52° angle, to 1 decimal place.

Answer: 7.1 cm

  1. sin 52° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 52°
  3. ≈ 7.1
4.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 60°. Find the side adjacent to the 60° angle, to 1 decimal place.

Answer: 6.5 cm

  1. cos 60° = adjacent ÷ hypotenuse
  2. adjacent = 13 × cos 60°
  3. ≈ 6.5
5.In a right-angled triangle, the hypotenuse is 23 cm and one angle is 21°. Find the side opposite the 21° angle, to 1 decimal place.

Answer: 8.2 cm

  1. sin 21° = opposite ÷ hypotenuse
  2. opposite = 23 × sin 21°
  3. ≈ 8.2
6.In a right-angled triangle, the hypotenuse is 5 cm and one angle is 58°. Find the side opposite the 58° angle, to 1 decimal place.

Answer: 4.2 cm

  1. sin 58° = opposite ÷ hypotenuse
  2. opposite = 5 × sin 58°
  3. ≈ 4.2
7.In a right-angled triangle, the hypotenuse is 22 cm and one angle is 61°. Find the side opposite the 61° angle, to 1 decimal place.

Answer: 19.2 cm

  1. sin 61° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 61°
  3. ≈ 19.2
8.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 22°. Find the side adjacent to the 22° angle, to 1 decimal place.

Answer: 18.5 cm

  1. cos 22° = adjacent ÷ hypotenuse
  2. adjacent = 20 × cos 22°
  3. ≈ 18.5
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