Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 59.0854°

Verified step by step guidance

1. Start with the given angle in decimal degrees: 59.0854°.
2. Separate the whole number part from the decimal part. Here, the whole number is 59°.
3. Convert the decimal part (0.0854) to minutes by multiplying by 60. This gives 0.0854 * 60 = 5.124 minutes.
4. Separate the whole number part from the decimal part of the minutes. Here, the whole number is 5'.
5. Convert the remaining decimal part (0.124) to seconds by multiplying by 60. This gives 0.124 * 60 seconds. Round this to the nearest second if necessary.

Key Concepts

Angle Conversion

Angle conversion involves changing an angle from one unit of measurement to another, such as from decimal degrees to degrees, minutes, and seconds (DMS). In DMS, one degree is divided into 60 minutes, and each minute is further divided into 60 seconds. This conversion is essential for precise measurements in various applications, including navigation and astronomy.

Decimal Degrees

Decimal degrees represent angles in a single numerical format, where the whole number part indicates degrees and the decimal part represents a fraction of a degree. For example, 59.0854° means 59 degrees and a fraction of a degree. Understanding decimal degrees is crucial for converting to DMS, as it provides the starting point for the conversion process.

Rounding

Rounding is the process of adjusting a number to a specified degree of accuracy, often to simplify calculations or present data more clearly. In the context of angle conversion, rounding to the nearest second means adjusting the calculated seconds value to the closest whole number. This is important for ensuring that the final angle measurement is both accurate and easy to interpret.