To find the measure of angle BAC given the equation \(\sin^{-1}\left(\frac{3.1}{4.5}\right) = x\), follow these steps:
1. Calculate the Ratio:
- We start by calculating the ratio \(\frac{3.1}{4.5}\).
- \(\frac{3.1}{4.5}\) simplifies to approximately 0.6889.
2. Find the Inverse Sine (Arcsine):
- We need to find the angle \(x\) whose sine is 0.6889. This is done by applying the inverse sine (arcsine) function.
- \(\sin^{-1}(0.6889)\) gives us the angle in radians.
3. Convert Radians to Degrees:
- Once we have the angle in radians, we convert it to degrees since the question asks for the measure in degrees.
- When converted, this angle is approximately 43.5422 degrees.
4. Round to the Nearest Whole Degree:
- Finally, we round 43.5422 degrees to the nearest whole number.
- Rounding 43.5422 gives us 44 degrees.
Therefore, the measure of angle BAC rounded to the nearest whole degree is [tex]\(\boxed{44^\circ}\)[/tex].
