Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. -25.485°

Verified step by step guidance

1. Identify the given angle in decimal degrees: \(-25.485^\circ\).
2. Separate the angle into its degrees part and the decimal part. The degrees part is the integer portion, which is \(-25^\circ\).
3. Take the absolute value of the decimal part (ignore the negative sign for now) to convert it into minutes: multiply \(0.485\) by \(60\) to get the minutes.
4. Separate the minutes into its integer part and decimal part. The integer part is the minutes, and the decimal part will be converted into seconds by multiplying by \(60\).
5. Combine the degrees, minutes, and seconds, and then reapply the negative sign to the degrees to reflect the original angle's direction.

Key Concepts

Decimal Degrees to Degrees, Minutes, and Seconds Conversion

This concept involves converting an angle expressed in decimal degrees into degrees, minutes, and seconds (D° M' S"). One degree equals 60 minutes, and one minute equals 60 seconds. The integer part of the decimal degree is the degrees, the decimal remainder multiplied by 60 gives minutes, and the remaining decimal part of minutes multiplied by 60 gives seconds.

Handling Negative Angles in Angle Conversion

When converting negative angles, the sign applies to the degrees, while minutes and seconds remain positive values. This means the angle is measured in the opposite direction, but minutes and seconds are always expressed as positive quantities to maintain clarity in the angle's components.

Rounding to the Nearest Second

After calculating seconds from the decimal part of minutes, rounding to the nearest whole number is necessary for precision. This ensures the angle is expressed in a standard format, making it easier to interpret and use in further calculations or applications.