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Year 9 Trigonometry (Finding Sides) Worksheet — Level 3 — 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 3 — 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 23 cm and one angle is 55°. Find the side opposite the 55° angle, to 1 decimal place.

Answer: 18.8 cm

  1. sin 55° = opposite ÷ hypotenuse
  2. opposite = 23 × sin 55°
  3. ≈ 18.8
2.In a right-angled triangle, the side adjacent to a 27° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 4.6 m

  1. tan 27° = opposite ÷ adjacent
  2. opposite = 9 × tan 27°
  3. ≈ 4.6
3.In a right-angled triangle, the side adjacent to a 26° angle is 14 m. Find the opposite side, to 1 decimal place.

Answer: 6.8 m

  1. tan 26° = opposite ÷ adjacent
  2. opposite = 14 × tan 26°
  3. ≈ 6.8
4.In a right-angled triangle, the side adjacent to a 39° angle is 20 m. Find the opposite side, to 1 decimal place.

Answer: 16.2 m

  1. tan 39° = opposite ÷ adjacent
  2. opposite = 20 × tan 39°
  3. ≈ 16.2
5.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 24°. Find the side adjacent to the 24° angle, to 1 decimal place.

Answer: 26.5 cm

  1. cos 24° = adjacent ÷ hypotenuse
  2. adjacent = 29 × cos 24°
  3. ≈ 26.5
6.In a right-angled triangle, the side adjacent to a 58° angle is 8 m. Find the opposite side, to 1 decimal place.

Answer: 12.8 m

  1. tan 58° = opposite ÷ adjacent
  2. opposite = 8 × tan 58°
  3. ≈ 12.8
7.In a right-angled triangle, the side adjacent to a 46° angle is 4 m. Find the opposite side, to 1 decimal place.

Answer: 4.1 m

  1. tan 46° = opposite ÷ adjacent
  2. opposite = 4 × tan 46°
  3. ≈ 4.1
8.In a right-angled triangle, the side adjacent to a 63° angle is 21 m. Find the opposite side, to 1 decimal place.

Answer: 41.2 m

  1. tan 63° = opposite ÷ adjacent
  2. opposite = 21 × tan 63°
  3. ≈ 41.2
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