In Exercises 25 to 30, use a calculator to convert each DMS measure to its equivalent decimal de

In Exercises 25 to 30, use a calculator to convert each DMS...

Key Concepts

Degrees, Minutes, and Seconds (DMS)

DMS is a system for expressing angles using degrees, minutes, and seconds. Each complete circle is divided into 360 degrees, every degree is further subdivided into 60 minutes, and each minute is divided into 60 seconds. This notation is commonly used in fields such as geography, astronomy, and navigation.

Decimal Degree Conversion

Decimal degree conversion involves expressing the angle entirely in degrees, where the minutes and seconds are converted into fractional degrees. This is done by dividing the number of minutes by 60 and the number of seconds by 3600, then adding these values to the whole degrees.

Unit Conversion Ratios

The conversion relies on the fixed ratios: 1 minute equals 1/60 of a degree and 1 second equals 1/3600 of a degree. These ratios allow for the precise transformation of angles from the DMS system to the decimal degree system.

Transcript

00:01 All right, number 30, we're given the angle 19 degrees, 12 minutes, 18 seconds, and we want to convert it just to degrees.

00:14 So basically, we need to figure out what portion of a degree, 12 minutes, and 18 seconds makes up.

00:23 And it's very easy to do.

00:24 We're just going to use these little conversion formulas right there.

00:28 We already know that our answer is going to be 19.

00:33 Point something degrees we just got to figure out what that point something is and that's what we use those conversions for so let's talk about the minutes first each minute is one 60th of a degree right so if i have 12 minutes that's 1260th of a degree and if you want to reduce that down you can but see we're going to put everything in the calculator and just add it up so we want a decimal answer when we're all said and so there's no need to reduce them.

01:07 But if you recognize that that's one -fifth, then you want to write it as one -fifth a degree, then by all means, go ahead.

01:13 I'm not going to do that.

01:15 All right.

01:15 And then for seconds, we have 18 seconds.

01:20 Remember, each second is one -60th of a minute, which, and again, each minute is one -60th of a second.

01:28 So that's how we get this conversion, that one -second is one -thre600th of a degree.

01:35 So if we have 18 seconds, that's equivalent to 183600s of a degree...

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