We appreciate your visit to In ΔNOP given that p 70 inches n 97 inches and angle O 163 circ find angle N to the nearest degree. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
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°.
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