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Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — Answers

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

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Year 11 · Mathematics · Trigonometry

Year 11 Trigonometry (Finding Sides) Worksheet — Level 2 — Answers

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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 57° angle is 19 m. Find the opposite side, to 1 decimal place.

Answer: 29.3 m

  1. tan 57° = opposite ÷ adjacent
  2. opposite = 19 × tan 57°
  3. ≈ 29.3
2.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 63°. Find the side opposite the 63° angle, to 1 decimal place.

Answer: 13.4 cm

  1. sin 63° = opposite ÷ hypotenuse
  2. opposite = 15 × sin 63°
  3. ≈ 13.4
3.In a right-angled triangle, the side adjacent to a 39° angle is 22 m. Find the opposite side, to 1 decimal place.

Answer: 17.8 m

  1. tan 39° = opposite ÷ adjacent
  2. opposite = 22 × tan 39°
  3. ≈ 17.8
4.In a right-angled triangle, the hypotenuse is 13 cm and one angle is 59°. Find the side opposite the 59° angle, to 1 decimal place.

Answer: 11.1 cm

  1. sin 59° = opposite ÷ hypotenuse
  2. opposite = 13 × sin 59°
  3. ≈ 11.1
5.In a right-angled triangle, the hypotenuse is 6 cm and one angle is 69°. Find the side opposite the 69° angle, to 1 decimal place.

Answer: 5.6 cm

  1. sin 69° = opposite ÷ hypotenuse
  2. opposite = 6 × sin 69°
  3. ≈ 5.6
6.In a right-angled triangle, the side adjacent to a 20° angle is 16 m. Find the opposite side, to 1 decimal place.

Answer: 5.8 m

  1. tan 20° = opposite ÷ adjacent
  2. opposite = 16 × tan 20°
  3. ≈ 5.8
7.In a right-angled triangle, the side adjacent to a 44° angle is 7 m. Find the opposite side, to 1 decimal place.

Answer: 6.8 m

  1. tan 44° = opposite ÷ adjacent
  2. opposite = 7 × tan 44°
  3. ≈ 6.8
8.In a right-angled triangle, the hypotenuse is 8 cm and one angle is 37°. Find the side opposite the 37° angle, to 1 decimal place.

Answer: 4.8 cm

  1. sin 37° = opposite ÷ hypotenuse
  2. opposite = 8 × sin 37°
  3. ≈ 4.8
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