In Exercises 19 to 24, use a calculator to convert each decimal degree measure to its equivalent

In Exercises 19 to 24, use a calculator to convert each...

Key Concepts

Decimal Degrees

Decimal degrees express angles using a single number that includes both the whole degree and a fractional part. This format is commonly used for its simplicity and is the standard for many forms of scientific and engineering data.

Degrees, Minutes, and Seconds (DMS) Format

The DMS format breaks an angle into three components: whole degrees, minutes (with 1 degree equal to 60 minutes), and seconds (with 1 minute equal to 60 seconds). This hierarchical representation is useful in navigation, surveying, and applications that require high precision.

Conversion Process from Decimal Degrees to DMS

To convert from decimal degrees to DMS, first extract the whole number as the degree component. Then, multiply the remaining fractional part by 60 to obtain the minutes. Finally, take the fractional part of the minutes and multiply by 60 to compute the seconds. This systematic process provides a precise conversion between the two measurement formats.

Transcript

00:03 All right.

00:05 And number 24, we want to convert 224 .282 degrees into dms, which of course is degrees minutes and seconds.

00:19 Now, yes, there's a very quick way to just go right to a calculator and type in the number, your angle, and hit a couple buttons, and you'll have it.

00:27 And we're going to confirm our answer that way.

00:29 I just don't want to go right to that right now because there's really no instruction in that.

00:34 Let's talk about how to put it to dms real quick by hand.

00:39 And we just use these two conversion formulas over here, right? one degree is 60 minutes and one minute is 60 seconds.

00:47 So very easy to do.

00:49 The first thing you need to realize is that we already know part of our answer, right? the first part of our answer is going to be 224 degrees.

00:58 What we don't know is how that 0 .282 converts to minutes and seconds.

01:03 But that's all, that's the actual only part that you do any work with.

01:10 So let's take that 0 .282 degrees and multiply by 60.

01:18 And that will tell us the equivalent number of minutes.

01:21 And if you do that, you're going to get 16 .92.

01:24 Now, if that were a whole number, we'd be done.

01:29 But it's not.

01:30 We still have this to convert to, seconds.

01:37 But you see we do have the second part of our answer, right? 16 .92 minutes means we put 16 minutes here, and now we convert the 0 .92 minutes to seconds using the second conversion there...

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