Answer :
To determine the measure of angle BAC, we need to solve the equation given by \(\sin ^{-1}\left(\frac{3.1}{4.5}\right)=x\). Let's go through the steps to find the measure of this angle:
1. Calculate the ratio \(\frac{3.1}{4.5}\):
[tex]\[ \frac{3.1}{4.5} = 0.6888888889 \][/tex]
2. Find the inverse sine (\(\sin^{-1}\)) of the ratio:
The inverse sine of 0.6888888889 will give us the angle in radians.
[tex]\[ \sin^{-1}(0.6888888889) \approx 0.7599550856658455 \text{ radians} \][/tex]
3. Convert the angle from radians to degrees:
To convert radians to degrees, use the conversion factor: \(180^{\circ} / \pi\). Thus,
[tex]\[ \text{Angle in degrees} = 0.7599550856658455 \times \frac{180}{\pi} \approx 43.54221902815587^{\circ} \][/tex]
4. Round the result to the nearest whole degree:
[tex]\[ \text{Rounded angle} = 44^{\circ} \][/tex]
Therefore, the measure of angle BAC is \(44^{\circ}\).
Among the given options:
- \(0^{\circ}\)
- \(1^{\circ}\)
- \(44^{\circ}\)
- \(48^{\circ}\)
The correct answer is [tex]\(44^{\circ}\)[/tex].
1. Calculate the ratio \(\frac{3.1}{4.5}\):
[tex]\[ \frac{3.1}{4.5} = 0.6888888889 \][/tex]
2. Find the inverse sine (\(\sin^{-1}\)) of the ratio:
The inverse sine of 0.6888888889 will give us the angle in radians.
[tex]\[ \sin^{-1}(0.6888888889) \approx 0.7599550856658455 \text{ radians} \][/tex]
3. Convert the angle from radians to degrees:
To convert radians to degrees, use the conversion factor: \(180^{\circ} / \pi\). Thus,
[tex]\[ \text{Angle in degrees} = 0.7599550856658455 \times \frac{180}{\pi} \approx 43.54221902815587^{\circ} \][/tex]
4. Round the result to the nearest whole degree:
[tex]\[ \text{Rounded angle} = 44^{\circ} \][/tex]
Therefore, the measure of angle BAC is \(44^{\circ}\).
Among the given options:
- \(0^{\circ}\)
- \(1^{\circ}\)
- \(44^{\circ}\)
- \(48^{\circ}\)
The correct answer is [tex]\(44^{\circ}\)[/tex].
