Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 82° 30'

Verified step by step guidance

1. Understand that the angle is given in degrees and minutes: 82° 30'. Recall that 1 degree (°) equals 60 minutes (').
2. To convert the minutes to decimal degrees, use the formula: \(\text{Decimal Degrees} = \text{Degrees} + \frac{\text{Minutes}}{60}\).
3. Substitute the given values into the formula: \(82 + \frac{30}{60}\).
4. Simplify the fraction \(\frac{30}{60}\) to get 0.5, so the expression becomes \$82 + 0.5$.
5. Add the values to find the decimal degree measure, then round to the nearest thousandth if necessary.

Key Concepts

Degrees, Minutes, and Seconds (DMS) Notation

Angles can be expressed in degrees (°), minutes ('), and seconds ("), where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This notation is commonly used in navigation and surveying to represent precise angle measures.

Conversion from Minutes to Decimal Degrees

To convert minutes to decimal degrees, divide the number of minutes by 60 since there are 60 minutes in one degree. For example, 30 minutes equals 0.5 degrees, which is added to the whole degrees to get the decimal degree value.

Rounding Decimal Degrees

After converting to decimal degrees, rounding is often necessary for simplicity and clarity. Rounding to the nearest thousandth means keeping three digits after the decimal point, which balances precision and readability in angle measurements.