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10th Grade Trigonometry (Finding Sides) Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the 10th Grade trigonometry worksheet.

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10th 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 21 cm and one angle is 56°. Find the side opposite the 56° angle, to 1 decimal place.

Answer: 17.4 cm

  1. sin 56° = opposite ÷ hypotenuse
  2. opposite = 21 × sin 56°
  3. ≈ 17.4
2.In a right triangle, the hypotenuse is 6 cm and one angle is 38°. Find the side opposite the 38° angle, to 1 decimal place.

Answer: 3.7 cm

  1. sin 38° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 38°
  3. ≈ 3.7
3.In a right triangle, the hypotenuse is 6 cm and one angle is 46°. Find the side opposite the 46° angle, to 1 decimal place.

Answer: 4.3 cm

  1. sin 46° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 46°
  3. ≈ 4.3
4.In a right triangle, the hypotenuse is 15 cm and one angle is 24°. Find the side adjacent to the 24° angle, to 1 decimal place.

Answer: 13.7 cm

  1. cos 24° = adjacent ÷ hypotenuse
  2. adjacent = 15 × cos 24°
  3. ≈ 13.7
5.In a right triangle, the side adjacent to a 24° angle is 8 m. Find the opposite side, to 1 decimal place.

Answer: 3.6 m

  1. tan 24° = opposite ÷ adjacent
  2. opposite = 8 × tan 24°
  3. ≈ 3.6
6.In a right triangle, the hypotenuse is 22 cm and one angle is 46°. Find the side opposite the 46° angle, to 1 decimal place.

Answer: 15.8 cm

  1. sin 46° = opposite ÷ hypotenuse
  2. opposite = 22 × sin 46°
  3. ≈ 15.8
7.In a right triangle, the side adjacent to a 27° angle is 11 m. Find the opposite side, to 1 decimal place.

Answer: 5.6 m

  1. tan 27° = opposite ÷ adjacent
  2. opposite = 11 × tan 27°
  3. ≈ 5.6
8.In a right triangle, the hypotenuse is 7 cm and one angle is 59°. Find the side opposite the 59° angle, to 1 decimal place.

Answer: 6 cm

  1. sin 59° = opposite ÷ hypotenuse
  2. opposite = 7 × sin 59°
  3. ≈ 6
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