The equation [tex]\cos^{-1}\left(\frac{3.4}{10}\right) = x[/tex] can be used to determine the measure of angle BAC to the nearest whole degree.

A. [tex]19^{\circ}[/tex]
B. [tex]20^{\circ}[/tex]
C. [tex]70^{\circ}[/tex]
D. [tex]71^{\circ}[/tex]



Answer :

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]