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

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

1.In a right-angled triangle, the hypotenuse is 14 cm and one angle is 34°. Find the side opposite the 34° angle, to 1 decimal place.

Answer: 7.8 cm

  1. sin 34° = opposite ÷ hypotenuse
  2. opposite = 14 × sin 34°
  3. ≈ 7.8
2.In a right-angled triangle, the hypotenuse is 5 cm and one angle is 52°. Find the side adjacent to the 52° angle, to 1 decimal place.

Answer: 3.1 cm

  1. cos 52° = adjacent ÷ hypotenuse
  2. adjacent = 5 × cos 52°
  3. ≈ 3.1
3.In a right-angled triangle, the side adjacent to a 56° angle is 24 m. Find the opposite side, to 1 decimal place.

Answer: 35.6 m

  1. tan 56° = opposite ÷ adjacent
  2. opposite = 24 × tan 56°
  3. ≈ 35.6
4.In a right-angled triangle, the side adjacent to a 23° angle is 25 m. Find the opposite side, to 1 decimal place.

Answer: 10.6 m

  1. tan 23° = opposite ÷ adjacent
  2. opposite = 25 × tan 23°
  3. ≈ 10.6
5.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 37°. Find the side opposite the 37° angle, to 1 decimal place.

Answer: 6 cm

  1. sin 37° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 37°
  3. ≈ 6
6.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 31°. Find the side opposite the 31° angle, to 1 decimal place.

Answer: 9.8 cm

  1. sin 31° = opposite ÷ hypotenuse
  2. opposite = 19 × sin 31°
  3. ≈ 9.8
7.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 59°. Find the side opposite the 59° angle, to 1 decimal place.

Answer: 18 cm

  1. sin 59° = opposite ÷ hypotenuse
  2. opposite = 21 × sin 59°
  3. ≈ 18
8.In a right-angled triangle, the hypotenuse is 19 cm and one angle is 50°. Find the side adjacent to the 50° angle, to 1 decimal place.

Answer: 12.2 cm

  1. cos 50° = adjacent ÷ hypotenuse
  2. adjacent = 19 × cos 50°
  3. ≈ 12.2
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