Final answer:
In triangle NOP with given side lengths, we can use the Law of Cosines to find the measure of angle O. The measure is approximately 30.1 degrees.
Step-by-step explanation:
In triangle NOP, the measures of the sides are as follows: n = 62 inches, o = 55 inches, and p = 35 inches. To find the measure of angle O, we can use the Law of Cosines. This law states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of the lengths of those two sides and the cosine of the angle opposite the first side.
So, we have:
o^2 = n^2 + p^2 - 2np*cos(O)
Plugging in the values:
(55)^2 = (62)^2 + (35)^2 - 2*(62)*(35)*cos(O)
Simplifying the equation:
3025 = 3844 + 1225 - 2*(62)*(35)*cos(O)
Now, solve for cos(O):
cos(O) = (3844 + 1225 - 3025) / (2*(62)*(35))
cos(O) = 44 / 2170
O = arccos(44 / 2170)
O ≈ 30.1°