To find the measure of angle [tex]\( \text{BAC} \)[/tex] in degrees, let's carefully follow each step of the problem:
1. Given Information:
The value inside the arccosine function is:
[tex]\[
\frac{3.4}{10}
\][/tex]
2. Calculate the Arccosine:
We first need to determine the arccosine (inverse cosine) of this value. The result will give us the angle in radians.
Let [tex]\( \alpha \)[/tex] represent our angle in radians:
[tex]\[
\alpha = \cos^{-1}\left(\frac{3.4}{10}\right)
\][/tex]
3. Conversion from Radians to Degrees:
To convert [tex]\(\alpha\)[/tex] from radians to degrees, we use the conversion factor:
[tex]\[
1 \text{ radian} = \frac{180}{\pi} \text{ degrees}
\][/tex]
4. Determine Degree Measure:
Hence, the degree measure [tex]\( \theta \)[/tex] of angle BAC is:
[tex]\[
\theta = \alpha \times \frac{180}{\pi}
\][/tex]
5. Rounding to the Nearest Whole Degree:
The final step is to round the resulting degree measure to the nearest whole degree.
The calculated degree measure turns out to be approximately [tex]\( 70^\circ \)[/tex]. Hence, the measure of angle BAC rounded to the nearest whole degree is:
[tex]\[
\boxed{70^\circ}
\][/tex]
So the degree measure of angle BAC is 70°, and the correct answer from the given choices is:
[tex]\[
70^{\circ}
\][/tex]
