Final answer:
To find the measure of the angle nearest to 30 degrees in triangle NOP with given side lengths, we can use the Law of Cosines.
Step-by-step explanation:
In triangle NOP, we are given that p = 72 inches and o = 84 inches. We need to find the measure of the angle nearest to 30 degrees.
To solve this problem, we can use the Law of Cosines, which states that for a triangle with sides a, b, and c opposite angles A, B, and C respectively, the following equation holds:
c^2 = a^2 + b^2 - 2abcos(C)
In our triangle NOP, we can let N be the angle we are looking for. Using the given information, we have:
o^2 = p^2 + 84^2 - 2(72)(84)cos(N)
Solving for cos(N), we get:
cos(N) = (p^2 + 84^2 - o^2) / (2(72)(84))
cos(N) ≈ 0.4789
Taking the inverse cosine, we find that the measure of angle N is approximately 60.1 degrees.