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: \(174.255^\circ\).
2. The whole number part is the degrees. So, the degrees are \(174^\circ\).
3. To find the minutes, take the decimal part \(0.255\) and multiply it by 60: \(0.255 \times 60\).
4. The whole number part of the result from step 3 is the minutes.
5. To find the seconds, take the decimal part from step 3's result and multiply it by 60 again, then round to the nearest second.

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"). Degrees remain the integer part, minutes are obtained by multiplying the decimal remainder by 60, and seconds come from multiplying the new decimal remainder by 60 again. This method allows for a more precise and traditional representation of angles.

Rounding to the Nearest Second

After calculating the seconds in the D° M' S" format, rounding is applied to simplify the value to the nearest whole second. This step ensures the angle measurement is practical and easy to use, especially in fields like navigation or surveying where precision to the second is standard.

Understanding Angle Measurement Units

Degrees, minutes, and seconds are units used to measure angles, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This hierarchical structure helps express angles more precisely than decimal degrees alone, and is commonly used in trigonometry, astronomy, and geography.