Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 38° 42' 18"

Verified step by step guidance

1. Identify the components of the angle: degrees (°), minutes ('), and seconds ("). Here, the angle is 38° 42' 18".
2. Recall the conversion relationships: 1 minute (') = \(\frac{1}{60}\) degrees and 1 second (") = \(\frac{1}{3600}\) degrees.
3. Convert the minutes to decimal degrees by dividing the number of minutes by 60: \(42' = \frac{42}{60}\) degrees.
4. Convert the seconds to decimal degrees by dividing the number of seconds by 3600: \(18" = \frac{18}{3600}\) degrees.
5. Add the degrees, the converted minutes, and the converted seconds together to get the total angle in decimal degrees: \(38 + \frac{42}{60} + \frac{18}{3600}\). Then, round the result to the nearest thousandth of a degree if required.

Key Concepts

Degrees, Minutes, and Seconds (DMS) Notation

Angles can be expressed in degrees (°), minutes ('), and seconds ("), where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This notation is commonly used in navigation and surveying to represent precise angle measurements.

Conversion from DMS to Decimal Degrees

To convert an angle from degrees, minutes, and seconds to decimal degrees, divide the minutes by 60 and the seconds by 3600, then add these values to the degrees. This process converts the angle into a single decimal number representing degrees.

Rounding Decimal Values

After conversion, decimal degrees are often rounded to a specified precision, such as the nearest thousandth. Rounding ensures the result is concise and practical for further calculations or applications.