Final answer:
To find the length of n in triangle NOP, we can use the Law of Sines to set up an equation. By plugging in the given values and solving for n, we find that the length of n is approximately 2102 centimeters.
Step-by-step explanation:
To find the length of n in triangle NOP, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
By using the Law of Sines, we can set up the following equation:
(sin ∠N) / n = (sin ∠O) / p
Plugging in the given values, we get:
(sin 127°) / n = (sin 30°) / 870
Now, we can solve for n:
n = (sin 127° / sin 30°) * 870
Calculating this expression, we find that the length of n is approximately 2102 centimeters.