To convert [tex]\(45^\circ 30' 45''\)[/tex] into degrees, we will follow these steps:
1. Understand the components:
- Degrees ([tex]\(45^\circ \)[/tex])
- Minutes ([tex]\(30'\)[/tex])
- Seconds ([tex]\(45''\)[/tex])
2. Convert minutes to degrees:
- There are 60 minutes in a degree, so each minute is [tex]\(\frac{1}{60}\)[/tex] degrees.
- Therefore, [tex]\(30'\)[/tex] is equal to [tex]\(\frac{30}{60}\)[/tex] degrees.
- [tex]\(\frac{30}{60} = 0.5\)[/tex] degrees.
3. Convert seconds to degrees:
- There are 3600 seconds in a degree (60 minutes per degree and 60 seconds per minute, so [tex]\(60 \times 60 = 3600\)[/tex]).
- Each second is [tex]\(\frac{1}{3600}\)[/tex] degrees.
- Therefore, [tex]\(45''\)[/tex] is equal to [tex]\(\frac{45}{3600}\)[/tex] degrees.
- [tex]\(\frac{45}{3600} = 0.0125\)[/tex] degrees.
4. Sum up the degrees:
- Add the degrees, the converted minutes, and the converted seconds:
- Total degrees = [tex]\(45^\circ + 0.5^\circ + 0.0125^\circ\)[/tex].
5. Calculate the total:
- Total degrees = [tex]\(45 + 0.5 + 0.0125 = 45.5125^\circ\)[/tex].
So, [tex]\(45^\circ 30' 45''\)[/tex] converted into degrees is [tex]\(45.5125^\circ\)[/tex].
