Answer :
To find the measure of angle BAC, we can use the trigonometric relationship involving the sine function. Specifically, we'll use the inverse sine (arcsine) function to determine the angle. Let's proceed step by step.
1. Identify the known values:
- The length of the opposite side of the angle BAC is 3.1 units.
- The length of the hypotenuse in the triangle is 4.5 units.
2. Set up the sine equation:
[tex]\[ \sin(\text{angle BAC}) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{3.1}{4.5} \][/tex]
3. Calculate the ratio:
[tex]\[ \frac{3.1}{4.5} \approx 0.6889 \][/tex]
4. Use the inverse sine function to find the angle whose sine is 0.6889:
[tex]\[ \text{angle BAC} = \sin^{-1}(0.6889) \][/tex]
5. Convert this angle to degrees:
The inverse sine of 0.6889 yields an angle of approximately 43.922 degrees.
6. Round the angle to the nearest whole number:
[tex]\[ 43.922 \approx 44 \][/tex]
Therefore, the measure of angle BAC, rounded to the nearest whole degree, is [tex]\(44^\circ\)[/tex].
So, the correct answer from the provided options is:
[tex]\[ 44^{\circ} \][/tex]
1. Identify the known values:
- The length of the opposite side of the angle BAC is 3.1 units.
- The length of the hypotenuse in the triangle is 4.5 units.
2. Set up the sine equation:
[tex]\[ \sin(\text{angle BAC}) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{3.1}{4.5} \][/tex]
3. Calculate the ratio:
[tex]\[ \frac{3.1}{4.5} \approx 0.6889 \][/tex]
4. Use the inverse sine function to find the angle whose sine is 0.6889:
[tex]\[ \text{angle BAC} = \sin^{-1}(0.6889) \][/tex]
5. Convert this angle to degrees:
The inverse sine of 0.6889 yields an angle of approximately 43.922 degrees.
6. Round the angle to the nearest whole number:
[tex]\[ 43.922 \approx 44 \][/tex]
Therefore, the measure of angle BAC, rounded to the nearest whole degree, is [tex]\(44^\circ\)[/tex].
So, the correct answer from the provided options is:
[tex]\[ 44^{\circ} \][/tex]
