To solve the problem of converting the angle from radians to degrees and degrees to degrees, minutes format, follow these steps:
1. Convert radians to degrees:
The given angle is 5.25 radians. To convert from radians to degrees, we use the conversion factor [tex]\(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\)[/tex]. Therefore,
[tex]\[
\text{angle degrees} = 5.25 \times \left( \frac{180}{\pi} \right) \approx 300.8028424436822^\circ
\][/tex]
Rounding to 2 decimal places, we get:
[tex]\[
\text{angle degrees rounded} \approx 300.80^\circ
\][/tex]
2. Convert degrees to degrees, minutes format:
- The integer part of the degrees is 300°.
- To find the minutes, we take the decimal part and multiply by 60:
[tex]\[
\text{minutes} = (0.8028424436822) \times 60 \approx 48.170546620932 \approx 48.17'
\][/tex]
So, in degrees and minutes format, the angle is:
[tex]\[
300^\circ 48.17'
\][/tex]
3. Check which of the given options match the converted values:
Option A: [tex]\(16.49^\circ\)[/tex] does not match 300.80°.
Option B: [tex]\(300^\circ 48'\)[/tex] is very close to 300° 48.17'. Given the typical rounding in such problems, they can be considered matching.
Option C: [tex]\(16^\circ 24'\)[/tex] does not match 300° 48.17'.
Option D: [tex]\(300.80^\circ\)[/tex] matches exactly with the rounded conversion value we computed.
4. Summary of matching options:
- Option A: No
- Option B: Yes
- Option C: No
- Option D: Yes
Therefore, the angle measuring 5.25 radians corresponds to options B and D.
