Sure, let's go through a step-by-step solution for converting the given angles from degrees and minutes into decimal degrees.
### Part (a): [tex]\( 40^\circ 45' \)[/tex]
1. Identify the degrees and the minutes:
- Degrees ([tex]\(^\circ\)[/tex]): [tex]\( 40 \)[/tex]
- Minutes ([tex]\('\)[/tex]): [tex]\( 45 \)[/tex]
2. Convert minutes into degrees:
- There are 60 minutes in a degree. Therefore, to convert minutes into degrees, we divide the number of minutes by 60.
- [tex]\( 45' \)[/tex] is equivalent to [tex]\( \frac{45}{60} \)[/tex] degrees.
- [tex]\(\frac{45}{60} = 0.75\)[/tex] degrees.
3. Add the degrees and the converted minutes together:
- [tex]\( 40 \)[/tex] degrees + [tex]\( 0.75 \)[/tex] degrees = [tex]\( 40.75 \)[/tex] degrees.
So, [tex]\( 40^\circ 45' \)[/tex] is equivalent to [tex]\( 40.75 \)[/tex] degrees in decimal form.
### Part (b): [tex]\( 50^\circ 15' \)[/tex]
1. Identify the degrees and the minutes:
- Degrees ([tex]\(^\circ\)[/tex]): [tex]\( 50 \)[/tex]
- Minutes ([tex]\('\)[/tex]): [tex]\( 15 \)[/tex]
2. Convert minutes into degrees:
- Again, there are 60 minutes in a degree. So, we need to convert the minutes into degrees by dividing by 60.
- [tex]\( 15' \)[/tex] is equivalent to [tex]\( \frac{15}{60} \)[/tex] degrees.
- [tex]\(\frac{15}{60} = 0.25\)[/tex] degrees.
3. Add the degrees and the converted minutes together:
- [tex]\( 50 \)[/tex] degrees + [tex]\( 0.25 \)[/tex] degrees = [tex]\( 50.25 \)[/tex] degrees.
Thus, [tex]\( 50^\circ 15' \)[/tex] is equivalent to [tex]\( 50.25 \)[/tex] degrees in decimal form.
### Summary:
- [tex]\( 40^\circ 45' \)[/tex] converts to [tex]\( 40.75 \)[/tex] degrees.
- [tex]\( 50^\circ 15' \)[/tex] converts to [tex]\( 50.25 \)[/tex] degrees.
