To determine the degree measure of angle BAC, we follow these steps:
1. Understand the Problem: We are given an equation involving the arccosine function, [tex]\(\cos^{-1}\left(\frac{3.4}{10}\right) = x\)[/tex], and need to determine the degree measure of angle [tex]\(x\)[/tex].
2. Calculate the Radian Measure: The arccosine function gives us the angle in radians whose cosine value is [tex]\(\frac{3.4}{10}\)[/tex]. Using a calculator or a mathematical software, we find that:
[tex]\[
x = \cos^{-1}\left(\frac{3.4}{10}\right) \approx 1.2238794292677349 \text{ radians}
\][/tex]
3. Convert Radians to Degrees: Next, we need to convert the angle from radians to degrees. The formula for converting radians to degrees is:
[tex]\[
\text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right)
\][/tex]
Applying the formula:
[tex]\[
x \text{ (in degrees)} = 1.2238794292677349 \times \left(\frac{180}{\pi}\right) \approx 70.12312592992117 \text{ degrees}
\][/tex]
4. Round to the Nearest Whole Degree: Finally, we round the degree measure to the nearest whole number:
[tex]\[
70.12312592992117 \text{ degrees} \approx 70^\circ
\][/tex]
Therefore, the degree measure of angle BAC, rounded to the nearest whole degree, is [tex]\(70^\circ\)[/tex]. The correct answer is:
[tex]\[
\boxed{70^\circ}
\][/tex]
