Certainly! To express 72.5680 degrees in degrees, minutes, and seconds, we need to follow these steps:
1. Separate the Degrees:
The integral part of the given number is 72. This represents the degrees.
[tex]\[
72.5680^\circ \implies 72^\circ + 0.5680^\circ
\][/tex]
2. Convert the Decimal Part to Minutes:
Multiply the decimal part (0.5680) by 60 to convert it to minutes:
[tex]\[
0.5680 \times 60 = 34.08 \text{ minutes}
\][/tex]
The integral part of this result (34) represents the minutes. The remaining decimal (0.08) will be converted into seconds.
[tex]\[
0.5680^\circ \implies 34' + 0.08'
\][/tex]
3. Convert the Remaining Decimal Part to Seconds:
Multiply the remaining decimal part (0.08) by 60 to convert it to seconds:
[tex]\[
0.08 \times 60 = 4.8 \text{ seconds}
\][/tex]
Rounding this to the nearest whole number gives us 5 seconds.
[tex]\[
0.08' \implies 4.8'' \approx 5''
\][/tex]
4. Combine All Parts:
Now, putting it all together:
[tex]\[
72.5680^\circ = 72^\circ 34' 5''
\][/tex]
Thus, 72.5680 degrees is expressed in degrees, minutes, and seconds as:
[tex]\[
72^\circ 34' 5''
\][/tex]
