Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 274° 18' 59"

Verified step by step guidance

1. Start by understanding that the angle is given in degrees, minutes, and seconds (DMS). The format is 274° 18' 59", where 274 is degrees, 18 is minutes, and 59 is seconds.
2. Convert the minutes to degrees. Since there are 60 minutes in a degree, divide the minutes by 60: \(18' = \frac{18}{60}\) degrees.
3. Convert the seconds to degrees. Since there are 3600 seconds in a degree (60 seconds per minute and 60 minutes per degree), divide the seconds by 3600: \(59" = \frac{59}{3600}\) degrees.
4. Add the converted minutes and seconds to the degrees to get the total in decimal degrees: \(274 + \frac{18}{60} + \frac{59}{3600}\).
5. Round the result to the nearest thousandth of a degree, if necessary.

Key Concepts

Degrees, Minutes, and Seconds (DMS)

The DMS system is a way to express angles using degrees, minutes, and seconds. One degree is divided into 60 minutes, and one minute is further divided into 60 seconds. This system is commonly used in navigation and geography. Understanding how to convert between DMS and decimal degrees is essential for accurate angle measurement.

Conversion to Decimal Degrees

To convert an angle from DMS to decimal degrees, you add the degrees to the minutes divided by 60 and the seconds divided by 3600. The formula is: Decimal Degrees = Degrees + (Minutes/60) + (Seconds/3600). This conversion is crucial for calculations in trigonometry and other mathematical applications where decimal representation is required.

Rounding Numbers

Rounding is the process of adjusting the digits of a number to make it simpler while maintaining its value close to the original. In this context, rounding to the nearest thousandth means keeping three decimal places. This is important for precision in measurements and calculations, especially in fields like engineering and physics where accuracy is critical.