To find the measure of angle BAC, we start by using the inverse sine function as given in the equation [tex]\(\sin^{-1}\left(\frac{3.1}{4.5}\right) = x\)[/tex].
Here's the step-by-step process:
1. Set Up the Equation:
[tex]\[
\sin x = \frac{3.1}{4.5}
\][/tex]
2. Calculate the Ratio:
[tex]\[
\frac{3.1}{4.5} \approx 0.6889
\][/tex]
3. Apply the Inverse Sine Function:
[tex]\[
x = \sin^{-1}(0.6889)
\][/tex]
4. Convert to Degrees:
To find the measure of angle [tex]\(x\)[/tex] in degrees, we use the inverse sine function values.
5. Finding the Measure:
Solving [tex]\(\sin^{-1}(0.6889)\)[/tex] will give us the angle value in degrees. Based on the calculated value, the angle [tex]\(x\)[/tex] comes out to approximately [tex]\(43.7\)[/tex] degrees.
6. Round to the Nearest Whole Degree:
[tex]\[
\text{Rounding 43.7 to the nearest whole number gives us } 44^\circ
\][/tex]
Therefore, the measure of angle BAC rounded to the nearest whole degree is [tex]\(44^\circ\)[/tex].
So, the correct answer is [tex]\(44^\circ\)[/tex].
