Sure! Let's convert each of the given angles into sexagesimal seconds step-by-step.
### a) 20° 20'
1. Convert the degrees to seconds:
- There are 3600 seconds in one degree.
- Therefore, [tex]\(20\)[/tex] degrees is calculated as:
[tex]\[
20 \times 3600 = 72000 \text{ seconds}
\][/tex]
2. Convert the minutes to seconds:
- There are 60 seconds in one minute.
- Therefore, [tex]\(20\)[/tex] minutes is calculated as:
[tex]\[
20 \times 60 = 1200 \text{ seconds}
\][/tex]
3. Add the results from step 1 and step 2 to get the total number of seconds:
[tex]\[
72000 \text{ seconds} + 1200 \text{ seconds} = 73200 \text{ seconds}
\][/tex]
So, [tex]\(20° 20'\)[/tex] is [tex]\(73200\)[/tex] sexagesimal seconds.
### b) 10° 5' 10"
1. Convert the degrees to seconds:
- There are 3600 seconds in one degree.
- Therefore, [tex]\(10\)[/tex] degrees is calculated as:
[tex]\[
10 \times 3600 = 36000 \text{ seconds}
\][/tex]
2. Convert the minutes to seconds:
- There are 60 seconds in one minute.
- Therefore, [tex]\(5\)[/tex] minutes is calculated as:
[tex]\[
5 \times 60 = 300 \text{ seconds}
\][/tex]
3. Directly add the extra seconds ([tex]\(10\)[/tex] seconds).
4. Add the results from step 1, step 2, and step 3 to get the total number of seconds:
[tex]\[
36000 \text{ seconds} + 300 \text{ seconds} + 10 \text{ seconds} = 36310 \text{ seconds}
\][/tex]
So, [tex]\(10° 5' 10''\)[/tex] is [tex]\(36310\)[/tex] sexagesimal seconds.
### c) 12' 4"
1. Convert the minutes to seconds:
- There are 60 seconds in one minute.
- Therefore, [tex]\(12\)[/tex] minutes is calculated as:
[tex]\[
12 \times 60 = 720 \text{ seconds}
\][/tex]
2. Directly add the extra seconds ([tex]\(4\)[/tex] seconds).
3. Add the results from step 1 and step 2 to get the total number of seconds:
[tex]\[
720 \text{ seconds} + 4 \text{ seconds} = 724 \text{ seconds}
\][/tex]
So, [tex]\(12' 4''\)[/tex] is [tex]\(724\)[/tex] sexagesimal seconds.
To summarize:
- [tex]\(20° 20'\)[/tex] is [tex]\(73200\)[/tex] sexagesimal seconds.
- [tex]\(10° 5' 10''\)[/tex] is [tex]\(36310\)[/tex] sexagesimal seconds.
- [tex]\(12' 4''\)[/tex] is [tex]\(724\)[/tex] sexagesimal seconds.
