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

Answer sheet with worked solutions for the Year 10 trigonometry worksheet.

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Trigonometry

Year 10 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 side adjacent to a 49° angle is 20 m. Find the opposite side, to 1 decimal place.

Answer: 23 m

  1. tan 49° = opposite ÷ adjacent
  2. opposite = 20 × tan 49°
  3. ≈ 23
2.In a right-angled triangle, the hypotenuse is 30 cm and one angle is 65°. Find the side opposite the 65° angle, to 1 decimal place.

Answer: 27.2 cm

  1. sin 65° = opposite ÷ hypotenuse
  2. opposite = 30 × sin 65°
  3. ≈ 27.2
3.In a right-angled triangle, the side adjacent to a 65° angle is 18 m. Find the opposite side, to 1 decimal place.

Answer: 38.6 m

  1. tan 65° = opposite ÷ adjacent
  2. opposite = 18 × tan 65°
  3. ≈ 38.6
4.In a right-angled triangle, the side adjacent to a 60° angle is 22 m. Find the opposite side, to 1 decimal place.

Answer: 38.1 m

  1. tan 60° = opposite ÷ adjacent
  2. opposite = 22 × tan 60°
  3. ≈ 38.1
5.In a right-angled triangle, the side adjacent to a 63° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 37.3 m

  1. tan 63° = opposite ÷ adjacent
  2. opposite = 19 × tan 63°
  3. ≈ 37.3
6.In a right-angled triangle, the side adjacent to a 28° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 8.5 m

  1. tan 28° = opposite ÷ adjacent
  2. opposite = 16 × tan 28°
  3. ≈ 8.5
7.In a right-angled triangle, the hypotenuse is 16 cm and one angle is 43°. Find the side opposite the 43° angle, to 1 decimal place.

Answer: 10.9 cm

  1. sin 43° = opposite ÷ hypotenuse
  2. opposite = 16 × sin 43°
  3. ≈ 10.9
8.In a right-angled triangle, the hypotenuse is 21 cm and one angle is 42°. Find the side adjacent to the 42° angle, to 1 decimal place.

Answer: 15.6 cm

  1. cos 42° = adjacent ÷ hypotenuse
  2. adjacent = 21 × cos 42°
  3. ≈ 15.6
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