To solve this problem, let's go through the step-by-step process.
1. Given Problem:
We are given the sine value, 0.9563.
2. Determine the Angle in Radians:
To find the angle whose sine is 0.9563, we need to use the inverse sine function. Using the inverse sine function, we find that the angle in radians is approximately 1.274074087551001 radians.
3. Convert Radians to Degrees:
Next, we convert this angle from radians to degrees. To do so, we use the conversion factor where [tex]\( 1 \text{ radian} \approx 57.2958 \text{ degrees} \)[/tex]. Using this conversion,
[tex]\[
\text{angle\_degrees} \approx 1.274074087551001 \times 57.2958 \approx 72.9990680036537 \text{ degrees}
\][/tex]
4. Round to the Nearest Degree:
Finally, we need to round the calculated angle to the nearest degree. Thus,
[tex]\[
\text{nearest\_degree} \approx 73 \text{ degrees}
\][/tex]
Given these steps and calculations, the correct answer is:
b. 73°.
