Express 172.45 degrees as an angle to the nearest minute

Question

The question asks to the nearest minute, it also asks express 172.45 as an angle.

Answer 1

Hi Arslaan--

 

The minutes of an angle are the subdivisions of its degrees. Every degree can be divided into 60 minutes, and each of those minutes can be divided into 60 seconds. Which basically means that one degree can be divided into 3600 little tiny parts.

 

So the decimal form (0.45) you have above needs be converted into minutes and seconds (the 172 degrees will stay the same.)

 

So you have a proportion: 45/100 = ?/3600. The missing number works out to be 1620 seconds.

 

Divide that by 60 to get the number of minutes:

 

1620/60 = 27 minutes, with no remainder (i.e., no seconds)

 

To double check, you can say is 27/60 equal to 0.45?

 

Yes it is!

 

(The funny part is, the online converters come up with the answer "26 minutes and 60 seconds," but since 60 seconds is another minute, I'm not sure why it would come up that way...)

 

Anyway, hope this helps!

 

Matt in NY

Answer 2

There are 60 minutes in a degree, so .45 degree is .45*60 = 27 minutes. 

 

The symbol for minutes is '

 

 

So the answer would be 172° 27'