To determine the measure of angle [tex]\( \angle BAC \)[/tex] using the equation [tex]\(\sin^{-1}\left(\frac{3.1}{4.5}\right) = x\)[/tex], let's go through the steps needed to solve it.
1. Calculate the ratio inside the arcsine function:
[tex]\[
\frac{3.1}{4.5}
\][/tex]
Dividing 3.1 by 4.5 yields:
[tex]\[
\frac{3.1}{4.5} = 0.6888888888888889
\][/tex]
2. Determine the arcsine (inverse sine) of this ratio:
[tex]\[
x = \sin^{-1}(0.6888888888888889)
\][/tex]
This results in the value of [tex]\(x\)[/tex] being:
[tex]\[
x \approx 0.7599550856658455 \text{ radians}
\][/tex]
3. Convert the angle from radians to degrees:
Since 1 radian = [tex]\( \frac{180}{\pi} \)[/tex] degrees, we convert the angle by multiplying by [tex]\(\frac{180}{\pi}\)[/tex]:
[tex]\[
x \approx 0.7599550856658455 \times \frac{180}{\pi} \approx 43.54221902815587 \text{ degrees}
\][/tex]
4. Round the angle to the nearest whole degree:
Rounding 43.54221902815587 to the nearest whole number gives us:
[tex]\[
44^\circ
\][/tex]
Therefore, the measure of angle [tex]\( \angle BAC \)[/tex] is [tex]\( 44^\circ \)[/tex].
Given the multiple-choice options:
- [tex]\( 0^\circ \)[/tex]
- [tex]\( 1^\circ \)[/tex]
- [tex]\( 44^\circ \)[/tex]
- [tex]\( 48^\circ \)[/tex]
The correct answer is:
[tex]\[
\boxed{44^\circ}
\][/tex]
