To determine the measure of angle BAC, we need to solve the equation \(\sin ^{-1}\left(\frac{3.1}{4.5}\right)=x\).
1. Calculate the ratio: First, we evaluate the fraction \(\frac{3.1}{4.5}\). This represents the sine of angle BAC:
[tex]\[
\frac{3.1}{4.5} \approx 0.6889
\][/tex]
2. Apply the inverse sine function: Next, we find the angle \(x\) whose sine is approximately 0.6889. This involves using the inverse sine function, also known as arcsine:
[tex]\[
x = \sin^{-1}(0.6889)
\][/tex]
3. Convert radians to degrees: Usually, results from trigonometric functions are in radians, but we need the angle in degrees. Using the arcsine function, we can directly obtain the angle in degrees because standard calculators and many tools include a built-in conversion.
4. Calculate the measure of angle BAC: We find that:
[tex]\[
x \approx 44.03^\circ
\][/tex]
5. Round to the nearest whole degree: Finally, we round 44.03° to the nearest whole degree:
[tex]\[
x \approx 44^\circ
\][/tex]
Thus, the measure of angle BAC is [tex]\(\boxed{44^\circ}\)[/tex].
