In \( \triangle N O P, n=62 \) inches, \( o=55 \) inches and \( p=35 \) inches. Find the measure of \( \angle O \) to the nearest 10 th of a degree.

To find the measure of \( \angle O \) in \( \triangle NOP \) with sides \( n = 62 \) inches, \( o = 55 \) inches, and \( p = 35 \) inches, we'll use the **Law of Cosines**. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles: \[ \cos O = \frac{n^2 + p^2 - o^2}{2np} \] **Step-by-Step Calculation:** 1. **Calculate the squares of the sides:** \[ n^2 = 62^2 = 3844 \\ p^2 = 35^2 = 1225 \\ o^2 = 55^2 = 3025 \] 2. **Plug these values into the formula:** \[ \cos O = \frac{3844 + 1225 - 3025}{2 \times 62 \times 35} = \frac{2044}{4340} \] 3. **Simplify the fraction:** \[ \cos O = \frac{2044}{4340} \approx 0.4710 \] 4. **Find the angle \( O \) using the inverse cosine function:** \[ O = \cos^{-1}(0.4710) \approx 61.9^\circ \] **Final Answer:** The measure of \( \angle O \) is approximately **61.9 degrees**.