Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 174.255°

Verified step by step guidance

1. Start with the given angle in decimal degrees: 174.255°.
2. Separate the whole number part from the decimal part: 174° and 0.255°.
3. Convert the decimal part to minutes by multiplying by 60: 0.255° × 60 = 15.3'.
4. Separate the whole number part from the decimal part of the minutes: 15' and 0.3'.
5. Convert the decimal part of the minutes to seconds by multiplying by 60: 0.3' × 60.

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.

Degrees, Minutes, and Seconds (DMS)

Degrees, minutes, and seconds is a way to express angles where degrees are the whole number part, minutes are the fractional part of a degree multiplied by 60, and seconds are the fractional part of a minute multiplied by 60. For example, 174.255° can be converted to DMS by separating the whole number from the decimal and calculating the corresponding minutes and seconds, providing a more detailed representation of the angle.

Rounding

Rounding is the process of adjusting a number to a specified degree of accuracy. In the context of angle conversion, rounding to the nearest second means determining the closest whole second value when converting from decimal degrees to DMS. This is important for ensuring that the final angle measurement is both accurate and practical for use in real-world applications.