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

Answer sheet with worked solutions for the 11th Grade trigonometry worksheet.

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11th Grade 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 triangle, the hypotenuse is 17 cm and one angle is 41°. Find the side opposite the 41° angle, to 1 decimal place.

Answer: 11.2 cm

  1. sin 41° = opposite ÷ hypotenuse
  2. opposite = 17 × sin 41°
  3. ≈ 11.2
2.In a right triangle, the side adjacent to a 38° angle is 13 m. Find the opposite side, to 1 decimal place.

Answer: 10.2 m

  1. tan 38° = opposite ÷ adjacent
  2. opposite = 13 × tan 38°
  3. ≈ 10.2
3.In a right triangle, the hypotenuse is 16 cm and one angle is 48°. Find the side opposite the 48° angle, to 1 decimal place.

Answer: 11.9 cm

  1. sin 48° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 48°
  3. ≈ 11.9
4.In a right triangle, the side adjacent to a 33° angle is 12 m. Find the opposite side, to 1 decimal place.

Answer: 7.8 m

  1. tan 33° = opposite ÷ adjacent
  2. opposite = 12 × tan 33°
  3. ≈ 7.8
5.In a right triangle, the side adjacent to a 23° angle is 7 m. Find the opposite side, to 1 decimal place.

Answer: 3 m

  1. tan 23° = opposite ÷ adjacent
  2. opposite = 7 × tan 23°
  3. ≈ 3
6.In a right triangle, the hypotenuse is 25 cm and one angle is 57°. Find the side adjacent to the 57° angle, to 1 decimal place.

Answer: 13.6 cm

  1. cos 57° = adjacent ÷ hypotenuse
  2. adjacent = 25 × cos 57°
  3. ≈ 13.6
7.In a right triangle, the hypotenuse is 11 cm and one angle is 28°. Find the side opposite the 28° angle, to 1 decimal place.

Answer: 5.2 cm

  1. sin 28° = opposite ÷ hypotenuse
  2. opposite = 11 × sin 28°
  3. ≈ 5.2
8.In a right triangle, the hypotenuse is 22 cm and one angle is 22°. Find the side adjacent to the 22° angle, to 1 decimal place.

Answer: 20.4 cm

  1. cos 22° = adjacent ÷ hypotenuse
  2. adjacent = 22 × cos 22°
  3. ≈ 20.4
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