To find the value of \(\arccos\left(\frac{11.5}{16}\right)\), we first need to ensure that the argument is within the domain of the arccosine function, which is \([-1, 1]\).

Here, \(\frac{11.5}{16} = 0.71875\), which is within the domain of the arccosine function.

Now, we can find the value of \(\arccos(0.71875)\):

\[
\arccos(0.71875) \approx 0.7705 \text{ radians}
\]

This value is in radians. If you need it in degrees, you can convert it using the conversion factor \( \frac{180}{\pi} \):

\[
0.7705 \text{ radians} \times \frac{180}{\pi} \approx 44.14^\circ
\]

So, \(\arccos(0.71875) \approx 0.7705\) radians or approximately \(44.14^\circ\).

Would you like further details or have any questions?

Here are 5 more questions you might be interested in:

1. How do you convert between radians and degrees?
2. What is the domain and range of the arccosine function?
3. How do you find the arccosine of a value using a calculator?
4. Can you explain the difference between arccosine and cosine?
5. What are some applications of the arccosine function in real life?

**Tip:** When using trigonometric functions, always make sure the input value is within the valid domain for that function.

Learn how to calculate arccos(11.5/16) using trigonometric principles. Understand the domain of the arccosine function, conversion between radians and degrees, and its application in mathematics. Suitable for advanced high school students and beyond.

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