Question

In △NOP, N=62 inches, O=55 inches, and P=35 inches. Find the measure of ∠O to the nearest 10th of a degree.

a) 46.6∘
b) 53.4∘
c) 63.4∘
d)73.2∘

Answer 1

To find the measure of angle O in triangle NOP, we can use the Law of Cosines.

This correct answer is b)

Step-by-step explanation:

To find the measure of angle O in triangle NOP, we can use the Law of Cosines. The Law of Cosines states that in any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds: c^2 = a^2 + b^2 - 2ab*cos(C).

In this case, we have side NO (a) with a length of 62 inches, side OP (b) with a length of 35 inches, and side NP (c) with a length of 55 inches. Let's substitute these values into the equation and solve for cos(O).

55^2 = 62^2 + 35^2 - 2*62*35*cos(O)

3025 = 3844 + 1225 - 4340*cos(O)

-244 = -4340*cos(O)

cos(O) = -244 / -4340

Using inverse cosine, we find that O is approximately equal to 53.4 degrees.

This correct answer is b)