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

Question

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

UpStudy AI · Accepted Answer

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**.
The measure of angle $$ \angle O $$ is approximately **61.9 degrees**.

In inches, inches and inches. Find the measure of to the nearest 10 th of a degree.

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