Answer :
To determine the measure of angle BAC, we start by solving the equation:
[tex]\[ \sin^{-1}\left(\frac{3.1}{4.5}\right) = x \][/tex]
First, calculate the value inside the inverse sine function:
[tex]\[ \frac{3.1}{4.5} \approx 0.6889 \][/tex]
Next, find the angle whose sine is [tex]\(0.6889\)[/tex]. This requires calculating the inverse sine (or arc sine) of [tex]\(0.6889\)[/tex]:
[tex]\[ x = \sin^{-1}(0.6889) \][/tex]
This value, [tex]\(x\)[/tex], is in radians. For practical use, we then convert this angle from radians to degrees. The obtained angle in radians is approximately:
[tex]\[ x \approx 0.759955 \][/tex]
To convert the angle from radians to degrees, we use the conversion factor [tex]\(180/\pi\)[/tex]:
[tex]\[ \text{Angle in degrees} = 0.759955 \times \left(\frac{180}{\pi}\right) \approx 43.5422 \][/tex]
Finally, round this angle to the nearest whole degree:
[tex]\[ \text{Rounded angle} \approx 44^\circ \][/tex]
Thus, the measure of angle BAC is:
[tex]\[ \boxed{44^\circ} \][/tex]
[tex]\[ \sin^{-1}\left(\frac{3.1}{4.5}\right) = x \][/tex]
First, calculate the value inside the inverse sine function:
[tex]\[ \frac{3.1}{4.5} \approx 0.6889 \][/tex]
Next, find the angle whose sine is [tex]\(0.6889\)[/tex]. This requires calculating the inverse sine (or arc sine) of [tex]\(0.6889\)[/tex]:
[tex]\[ x = \sin^{-1}(0.6889) \][/tex]
This value, [tex]\(x\)[/tex], is in radians. For practical use, we then convert this angle from radians to degrees. The obtained angle in radians is approximately:
[tex]\[ x \approx 0.759955 \][/tex]
To convert the angle from radians to degrees, we use the conversion factor [tex]\(180/\pi\)[/tex]:
[tex]\[ \text{Angle in degrees} = 0.759955 \times \left(\frac{180}{\pi}\right) \approx 43.5422 \][/tex]
Finally, round this angle to the nearest whole degree:
[tex]\[ \text{Rounded angle} \approx 44^\circ \][/tex]
Thus, the measure of angle BAC is:
[tex]\[ \boxed{44^\circ} \][/tex]
