To determine the measure of angle BAC, which is given by the equation [tex]\(\cos^{-1}\left(\frac{3.4}{10}\right) = x\)[/tex], we'll follow these steps:
1. Calculate the ratio:
[tex]\[\frac{3.4}{10} = 0.34\][/tex]
2. Find the angle in radians:
[tex]\(\cos^{-1}(0.34)\)[/tex] or [tex]\(\arccos(0.34)\)[/tex] gives us the measure of the angle in radians.
Through calculations, we find:
[tex]\[ \arccos(0.34) \approx 1.2238794292677349 \text{ radians} \][/tex]
3. Convert the angle from radians to degrees:
To convert radians to degrees, use the conversion factor that [tex]\(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\)[/tex].
[tex]\[
1.2238794292677349 \text{ radians} \times \frac{180}{\pi} \approx 70.12312592992117 \text{ degrees}
\][/tex]
4. Round to the nearest whole degree:
The angle in degrees is approximately [tex]\(70.12312592992117\)[/tex]. Rounding this to the nearest whole number gives us:
[tex]\[70^\circ\][/tex]
Therefore, the measure of angle BAC to the nearest whole degree is:
[tex]\[
\boxed{70^\circ}
\][/tex]
