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In ΔNOP, p = 70 inches, n = 97 inches and ∠O=163°. Find ∠N, to the nearest degree.

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Answer:

  • 10°

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In ΔNOP, we are given:

  • p = 70 inches,
  • n = 97 inches,
  • ∠O = 163°

Use the law of cosines to find side o:

  • o² = n² + p² - 2(np)cos(∠O)
  • o² = 97² + 70² - 2(97)(70)cos(163°)
  • o² = 27295.61
  • o = 165.2

Now, use the law of sines to find ∠N:

  • sin(∠N) / n = sin(∠O) / o
  • sin(∠N) / 97 = sin(163°) / 165.2
  • sin(∠N) = 97*sin(163°) / 165.2
  • sin(∠N) = 0.17
  • m∠N = arcsin (0.17)
  • m∠N = 9.78° ≈ 10°

So, ∠N is approximately 10°.

User Albert Gareev
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