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Year 10 Trigonometry (Finding Sides) Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the Year 10 trigonometry worksheet.

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Year 10 · Mathematics · Trigonometry

Year 10 Trigonometry (Finding Sides) Worksheet — Level 2 — Answers

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

1.In a right-angled triangle, the hypotenuse is 24 cm and one angle is 63°. Find the side adjacent to the 63° angle, to 1 decimal place.

Answer: 10.9 cm

  1. cos 63° = adjacent ÷ hypotenuse
  2. adjacent = 24 × cos 63°
  3. ≈ 10.9
2.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 53°. Find the side adjacent to the 53° angle, to 1 decimal place.

Answer: 17.5 cm

  1. cos 53° = adjacent ÷ hypotenuse
  2. adjacent = 29 × cos 53°
  3. ≈ 17.5
3.In a right-angled triangle, the side adjacent to a 52° angle is 14 m. Find the opposite side, to 1 decimal place.

Answer: 17.9 m

  1. tan 52° = opposite ÷ adjacent
  2. opposite = 14 × tan 52°
  3. ≈ 17.9
4.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 38°. Find the side adjacent to the 38° angle, to 1 decimal place.

Answer: 22.9 cm

  1. cos 38° = adjacent ÷ hypotenuse
  2. adjacent = 29 × cos 38°
  3. ≈ 22.9
5.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 47°. Find the side adjacent to the 47° angle, to 1 decimal place.

Answer: 19.8 cm

  1. cos 47° = adjacent ÷ hypotenuse
  2. adjacent = 29 × cos 47°
  3. ≈ 19.8
6.In a right-angled triangle, the side adjacent to a 37° angle is 12 m. Find the opposite side, to 1 decimal place.

Answer: 9 m

  1. tan 37° = opposite ÷ adjacent
  2. opposite = 12 × tan 37°
  3. ≈ 9
7.In a right-angled triangle, the hypotenuse is 29 cm and one angle is 29°. Find the side adjacent to the 29° angle, to 1 decimal place.

Answer: 25.4 cm

  1. cos 29° = adjacent ÷ hypotenuse
  2. adjacent = 29 × cos 29°
  3. ≈ 25.4
8.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 61°. Find the side adjacent to the 61° angle, to 1 decimal place.

Answer: 7.8 cm

  1. cos 61° = adjacent ÷ hypotenuse
  2. adjacent = 16 × cos 61°
  3. ≈ 7.8
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