To determine the measure of angle BAC, we start by solving the equation:
[tex]\[
\sin^{-1}\left(\frac{3.1}{4.5}\right) = x
\][/tex]
First, calculate the value inside the inverse sine function:
[tex]\[
\frac{3.1}{4.5} \approx 0.6889
\][/tex]
Next, find the angle whose sine is [tex]\(0.6889\)[/tex]. This requires calculating the inverse sine (or arc sine) of [tex]\(0.6889\)[/tex]:
[tex]\[
x = \sin^{-1}(0.6889)
\][/tex]
This value, [tex]\(x\)[/tex], is in radians. For practical use, we then convert this angle from radians to degrees. The obtained angle in radians is approximately:
[tex]\[
x \approx 0.759955
\][/tex]
To convert the angle from radians to degrees, we use the conversion factor [tex]\(180/\pi\)[/tex]:
[tex]\[
\text{Angle in degrees} = 0.759955 \times \left(\frac{180}{\pi}\right) \approx 43.5422
\][/tex]
Finally, round this angle to the nearest whole degree:
[tex]\[
\text{Rounded angle} \approx 44^\circ
\][/tex]
Thus, the measure of angle BAC is:
[tex]\[
\boxed{44^\circ}
\][/tex]
