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

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

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Trigonometry

Year 9 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 2 — 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 40°. Find the side adjacent to the 40° angle, to 1 decimal place.

Answer: 17.6 cm

  1. cos 40° = adjacent ÷ hypotenuse
  2. adjacent = 23 × cos 40°
  3. ≈ 17.6
2.In a right-angled triangle, the side adjacent to a 47° angle is 17 m. Find the opposite side, to 1 decimal place.

Answer: 18.2 m

  1. tan 47° = opposite ÷ adjacent
  2. opposite = 17 × tan 47°
  3. ≈ 18.2
3.In a right-angled triangle, the hypotenuse is 26 cm and one angle is 29°. Find the side adjacent to the 29° angle, to 1 decimal place.

Answer: 22.7 cm

  1. cos 29° = adjacent ÷ hypotenuse
  2. adjacent = 26 × cos 29°
  3. ≈ 22.7
4.In a right-angled triangle, the side adjacent to a 59° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 15 m

  1. tan 59° = opposite ÷ adjacent
  2. opposite = 9 × tan 59°
  3. ≈ 15
5.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 63°. Find the side opposite the 63° angle, to 1 decimal place.

Answer: 16.9 cm

  1. sin 63° = opposite ÷ hypotenuse
  2. opposite = 19 × sin 63°
  3. ≈ 16.9
6.In a right-angled triangle, the side adjacent to a 58° angle is 25 m. Find the opposite side, to 1 decimal place.

Answer: 40 m

  1. tan 58° = opposite ÷ adjacent
  2. opposite = 25 × tan 58°
  3. ≈ 40
7.In a right-angled triangle, the side adjacent to a 65° angle is 12 m. Find the opposite side, to 1 decimal place.

Answer: 25.7 m

  1. tan 65° = opposite ÷ adjacent
  2. opposite = 12 × tan 65°
  3. ≈ 25.7
8.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 22°. Find the side opposite the 22° angle, to 1 decimal place.

Answer: 7.9 cm

  1. sin 22° = opposite ÷ hypotenuse
  2. opposite = 21 × sin 22°
  3. ≈ 7.9
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