15)
(a) Find 28° 29’ 46” - 16° 48’ 59’’
(b) Express 5.4° in terms of
- degrees
- minutes
- seconds
Do you know how many minutes in a degree (60) and how many seconds in a minute (60)?
That should help you with the problems.
(a) To find the difference between two angles given in degrees, minutes, and seconds, we need to subtract the degrees, minutes, and seconds separately.
Given:
Angle A = 28° 29' 46"
Angle B = 16° 48' 59"
Subtracting the degrees:
28° - 16° = 12°
Subtracting the minutes:
29' - 48' = -19'
Subtracting the seconds:
46" - 59" = -13"
Now, we have:
12° - 19' - 13"
However, since the minutes and seconds are negative, we need to carry out a borrow.
Subtracting from 60:
60' - 19' = 41'
60" - 13" = 47"
Our final answer is:
12° 41' 47"
(b) To express 5.4° in terms of degrees, minutes, and seconds, we need to convert the decimal degree to minutes and seconds.
Given:
Angle = 5.4°
Converting to minutes:
Multiply the decimal part by 60:
0.4 * 60 = 24 minutes
Converting to seconds:
Multiply the decimal part by 60:
0.4 * 60 = 24 seconds
Therefore, 5.4° is equivalent to:
5° 24' 24"