Final answer:
To find the length of side N in triangle NOP with given angles and side length P, we use the Law of Sines and solve for N, then round the result to the nearest centimeter.
Step-by-step explanation:
The question asks to find the length of side N in triangle NOP given P = 870 cm, ∠N = 127°, and ∠O = 30°. By the Law of Sines, we have:
sin(∠N) / N = sin(∠O) / P
Substituting the given values:
sin(127°) / N = sin(30°) / 870
Since sin(30°) is 0.5, we simplify to:
sin(127°) / N = 0.5 / 870
After calculating sin(127°) and solving for N, we can find the length rounded to the nearest centimeter.