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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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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 21 cm and one angle is 36°. Find the side adjacent to the 36° angle, to 1 decimal place.

Answer: 17 cm

  1. cos 36° = adjacent ÷ hypotenuse
  2. adjacent = 21 × cos 36°
  3. ≈ 17
2.In a right-angled triangle, the hypotenuse is 11 cm and one angle is 41°. Find the side adjacent to the 41° angle, to 1 decimal place.

Answer: 8.3 cm

  1. cos 41° = adjacent ÷ hypotenuse
  2. adjacent = 11 × cos 41°
  3. ≈ 8.3
3.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 35°. Find the side opposite the 35° angle, to 1 decimal place.

Answer: 5.7 cm

  1. sin 35° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 35°
  3. ≈ 5.7
4.In a right-angled triangle, the hypotenuse is 20 cm and one angle is 37°. Find the side adjacent to the 37° angle, to 1 decimal place.

Answer: 16 cm

  1. cos 37° = adjacent ÷ hypotenuse
  2. adjacent = 20 × cos 37°
  3. ≈ 16
5.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 47°. Find the side opposite the 47° angle, to 1 decimal place.

Answer: 15.4 cm

  1. sin 47° = opposite ÷ hypotenuse
  2. opposite = 21 × sin 47°
  3. ≈ 15.4
6.In a right-angled triangle, the hypotenuse is 30 cm and one angle is 49°. Find the side opposite the 49° angle, to 1 decimal place.

Answer: 22.6 cm

  1. sin 49° = opposite ÷ hypotenuse
  2. opposite = 30 × sin 49°
  3. ≈ 22.6
7.In a right-angled triangle, the hypotenuse is 12 cm and one angle is 20°. Find the side opposite the 20° angle, to 1 decimal place.

Answer: 4.1 cm

  1. sin 20° = opposite ÷ hypotenuse
  2. opposite = 12 × sin 20°
  3. ≈ 4.1
8.In a right-angled triangle, the side adjacent to a 39° angle is 23 m. Find the opposite side, to 1 decimal place.

Answer: 18.6 m

  1. tan 39° = opposite ÷ adjacent
  2. opposite = 23 × tan 39°
  3. ≈ 18.6
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