To find the measure of angle [tex]\( BAC \)[/tex] given the equation [tex]\(\sin^{-1}\left(\frac{3.1}{4.5}\right) = x\)[/tex], we need to follow these steps:
1. Determine the ratio:
The ratio inside the inverse sine function is [tex]\(\frac{3.1}{4.5}\)[/tex].
2. Calculate the inverse sine:
We use the ratio calculated above and find the angle whose sine value is [tex]\(\frac{3.1}{4.5}\)[/tex]. This involves computing the inverse sine (or arcsine) of the ratio.
3. Convert to degrees:
The result from the inverse sine function (which is typically in radians) needs to be converted to degrees since standard angle measures are given in degrees.
4. Round to the nearest whole degree:
Finally, we round the computed angle to the nearest whole degree.
Let's summarize the numerical results:
- The angle [tex]\( x \approx 43.54221902815587^\circ \)[/tex].
- Rounded to the nearest whole degree, this gives [tex]\( 44^\circ \)[/tex].
Therefore, the measure of angle [tex]\( BAC \)[/tex] is approximately [tex]\( 44^\circ \)[/tex].
The answer is [tex]\( 44^\circ \)[/tex].
