To find the measure of angle BAC, we need to solve the equation [tex]\(\sin^{-1}\left(\frac{3.1}{4.5}\right) = x\)[/tex].
Here are the detailed steps:
1. Calculate the ratio:
[tex]\[
\frac{3.1}{4.5}
\][/tex]
This division gives us approximately 0.68888888889.
2. Use the arcsine function:
The arcsine (or inverse sine) function will give us the angle whose sine is the given ratio. Therefore, we calculate:
[tex]\[
x = \sin^{-1}(0.68888888889)
\][/tex]
This gives us an angle [tex]\(x\)[/tex] in radians.
3. Convert radians to degrees:
To convert from radians to degrees, we use the fact that [tex]\(\pi\)[/tex] radians is 180 degrees. Hence, we can convert as:
[tex]\[
x \text{ (in degrees)} = x \text{ (in radians)} \times \left( \frac{180}{\pi} \right)
\][/tex]
4. Determine the exact angle in degrees:
Using the provided answer, we know that the angle in radians calculated is approximately 0.7599550856658455 radians.
5. Convert the given radian measure to degrees:
The already calculated measure is approximately 43.54221902815587 degrees.
6. Round to the nearest whole degree:
Finally, we round 43.54221902815587 to the nearest whole degree, which is:
[tex]\[
44^\circ
\][/tex]
Thus, the measure of angle BAC is [tex]\(44^\circ\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{44^\circ}
\][/tex]
