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

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

1.In a right triangle, the hypotenuse is 30 cm and one angle is 26°. Find the side opposite the 26° angle, to 1 decimal place.

Answer: 13.2 cm

  1. sin 26° = opposite ÷ hypotenuse
  2. opposite = 30 × sin 26°
  3. ≈ 13.2
2.In a right triangle, the side adjacent to a 63° angle is 21 m. Find the opposite side, to 1 decimal place.

Answer: 41.2 m

  1. tan 63° = opposite ÷ adjacent
  2. opposite = 21 × tan 63°
  3. ≈ 41.2
3.In a right triangle, the hypotenuse is 7 cm and one angle is 68°. Find the side opposite the 68° angle, to 1 decimal place.

Answer: 6.5 cm

  1. sin 68° = opposite ÷ hypotenuse
  2. opposite = 7 × sin 68°
  3. ≈ 6.5
4.In a right triangle, the hypotenuse is 9 cm and one angle is 53°. Find the side adjacent to the 53° angle, to 1 decimal place.

Answer: 5.4 cm

  1. cos 53° = adjacent ÷ hypotenuse
  2. adjacent = 9 × cos 53°
  3. ≈ 5.4
5.In a right triangle, the hypotenuse is 12 cm and one angle is 26°. Find the side opposite the 26° angle, to 1 decimal place.

Answer: 5.3 cm

  1. sin 26° = opposite ÷ hypotenuse
  2. opposite = 12 × sin 26°
  3. ≈ 5.3
6.In a right triangle, the hypotenuse is 28 cm and one angle is 54°. Find the side opposite the 54° angle, to 1 decimal place.

Answer: 22.7 cm

  1. sin 54° = opposite ÷ hypotenuse
  2. opposite = 28 × sin 54°
  3. ≈ 22.7
7.In a right triangle, the hypotenuse is 15 cm and one angle is 21°. Find the side opposite the 21° angle, to 1 decimal place.

Answer: 5.4 cm

  1. sin 21° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 21°
  3. ≈ 5.4
8.In a right triangle, the side adjacent to a 27° angle is 7 m. Find the opposite side, to 1 decimal place.

Answer: 3.6 m

  1. tan 27° = opposite ÷ adjacent
  2. opposite = 7 × tan 27°
  3. ≈ 3.6
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