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Year 11 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 11 trigonometry worksheet.

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Year 11 Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 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 26 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 17.7 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 26 × sin 43°
  3. ≈ 17.7
2.In a right-angled triangle, the side adjacent to a 62° angle is 8 m. Find the opposite side, to 1 decimal place.

Answer: 15 m

  1. tan 62° = opposite ÷ adjacent
  2. opposite = 8 × tan 62°
  3. ≈ 15
3.In a right-angled triangle, the side adjacent to a 58° angle is 9 m. Find the opposite side, to 1 decimal place.

Answer: 14.4 m

  1. tan 58° = opposite ÷ adjacent
  2. opposite = 9 × tan 58°
  3. ≈ 14.4
4.In a right-angled triangle, the side adjacent to a 45° angle is 13 m. Find the opposite side, to 1 decimal place.

Answer: 13 m

  1. tan 45° = opposite ÷ adjacent
  2. opposite = 13 × tan 45°
  3. ≈ 13
5.In a right-angled triangle, the hypotenuse is 30 cm and one angle is 37°. Find the side adjacent to the 37° angle, to 1 decimal place.

Answer: 24 cm

  1. cos 37° = adjacent ÷ hypotenuse
  2. adjacent = 30 × cos 37°
  3. ≈ 24
6.In a right-angled triangle, the hypotenuse is 10 cm and one angle is 25°. Find the side opposite the 25° angle, to 1 decimal place.

Answer: 4.2 cm

  1. sin 25° = opposite ÷ hypotenuse
  2. opposite = 10 × sin 25°
  3. ≈ 4.2
7.In a right-angled triangle, the hypotenuse is 25 cm and one angle is 56°. Find the side adjacent to the 56° angle, to 1 decimal place.

Answer: 14 cm

  1. cos 56° = adjacent ÷ hypotenuse
  2. adjacent = 25 × cos 56°
  3. ≈ 14
8.In a right-angled triangle, the side adjacent to a 52° angle is 17 m. Find the opposite side, to 1 decimal place.

Answer: 21.8 m

  1. tan 52° = opposite ÷ adjacent
  2. opposite = 17 × tan 52°
  3. ≈ 21.8
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