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Year 10 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 4 — Answers

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

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Trigonometry

Year 10 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 10 cm and one angle is 44°. Find the side adjacent to the 44° angle, to 1 decimal place.

Answer: 7.2 cm

  1. cos 44° = adjacent ÷ hypotenuse
  2. adjacent = 10 × cos 44°
  3. ≈ 7.2
2.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 59°. Find the side opposite the 59° angle, to 1 decimal place.

Answer: 12 cm

  1. sin 59° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 59°
  3. ≈ 12
3.In a right-angled triangle, the side adjacent to a 31° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 5.4 m

  1. tan 31° = opposite ÷ adjacent
  2. opposite = 9 × tan 31°
  3. ≈ 5.4
4.In a right-angled triangle, the side adjacent to a 51° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 19.8 m

  1. tan 51° = opposite ÷ adjacent
  2. opposite = 16 × tan 51°
  3. ≈ 19.8
5.In a right-angled triangle, the hypotenuse is 17 cm and one angle is 38°. Find the side opposite the 38° angle, to 1 decimal place.

Answer: 10.5 cm

  1. sin 38° = opposite ÷ hypotenuse
  2. opposite = 17 × sin 38°
  3. ≈ 10.5
6.In a right-angled triangle, the hypotenuse is 9 cm and one angle is 24°. Find the side opposite the 24° angle, to 1 decimal place.

Answer: 3.7 cm

  1. sin 24° = opposite ÷ hypotenuse
  2. opposite = 9 × sin 24°
  3. ≈ 3.7
7.In a right-angled triangle, the side adjacent to a 27° angle is 21 m. Find the opposite side, to 1 decimal place.

Answer: 10.7 m

  1. tan 27° = opposite ÷ adjacent
  2. opposite = 21 × tan 27°
  3. ≈ 10.7
8.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 37°. Find the side adjacent to the 37° angle, to 1 decimal place.

Answer: 12 cm

  1. cos 37° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 37°
  3. ≈ 12
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