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Year 9 Trigonometry (Finding Sides) Worksheet — Level 2 — Practice Set 3 — 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 3 — Answers

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

1.In a right-angled triangle, the side adjacent to a 24° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 8.5 m

  1. tan 24° = opposite ÷ adjacent
  2. opposite = 19 × tan 24°
  3. ≈ 8.5
2.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 30°. Find the side adjacent to the 30° angle, to 1 decimal place.

Answer: 7.8 cm

  1. cos 30° = adjacent ÷ hypotenuse
  2. adjacent = 9 × cos 30°
  3. ≈ 7.8
3.In a right-angled triangle, the hypotenuse is 27 cm and one angle is 46°. Find the side opposite the 46° angle, to 1 decimal place.

Answer: 19.4 cm

  1. sin 46° = opposite ÷ hypotenuse
  2. opposite = 27 × sin 46°
  3. ≈ 19.4
4.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 51°. Find the side opposite the 51° angle, to 1 decimal place.

Answer: 11.7 cm

  1. sin 51° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 51°
  3. ≈ 11.7
5.In a right-angled triangle, the side adjacent to a 25° angle is 20 m. Find the opposite side, to 1 decimal place.

Answer: 9.3 m

  1. tan 25° = opposite ÷ adjacent
  2. opposite = 20 × tan 25°
  3. ≈ 9.3
6.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 58°. Find the side opposite the 58° angle, to 1 decimal place.

Answer: 11.9 cm

  1. sin 58° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 58°
  3. ≈ 11.9
7.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 30°. Find the side opposite the 30° angle, to 1 decimal place.

Answer: 6.5 cm

  1. sin 30° = opposite ÷ hypotenuse
  2. opposite = 13 × sin 30°
  3. ≈ 6.5
8.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 40°. Find the side opposite the 40° angle, to 1 decimal place.

Answer: 8.4 cm

  1. sin 40° = opposite ÷ hypotenuse
  2. opposite = 13 × sin 40°
  3. ≈ 8.4
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