To find the degree measure of angle [tex]\( \angle BAC \)[/tex], we start with the given equation [tex]\(\cos ^{-1}\left(\frac{3.4}{10}\right) = x\)[/tex]. Here are the steps we take:
1. Calculate the ratio inside the arccos function:
[tex]\[
\frac{3.4}{10} = 0.34
\][/tex]
2. Apply the arccos function to this ratio to find the angle [tex]\( x \)[/tex] in radians:
[tex]\[
x = \cos^{-1}(0.34)
\][/tex]
3. Convert this angle from radians to degrees:
Recall the conversion factor between degrees and radians:
[tex]\[
x \text{ (in degrees)} = x \text{ (in radians)} \times \left(\frac{180}{\pi}\right)
\][/tex]
4. Calculate the angle in degrees:
[tex]\[
x \approx 70.1231^\circ
\][/tex]
5. Round the angle to the nearest whole degree:
[tex]\[
x \approx 70^\circ
\][/tex]
Therefore, the measure of angle [tex]\( \angle BAC \)[/tex], when rounded to the nearest whole degree, is [tex]\( 70^\circ \)[/tex].
The correct option is:
[tex]\[
70^\circ
\][/tex]
