Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). ― 70° 48'

Verified step by step guidance

1. Understand that the angle is given in degrees and minutes, where 70° is the degree part and 48' is the minute part.
2. Recall that 1 degree is equal to 60 minutes. Therefore, to convert minutes to degrees, divide the number of minutes by 60.
3. Convert 48 minutes to degrees by calculating \( \frac{48}{60} \).
4. Add the converted minutes in degrees to the degree part: 70° + \( \frac{48}{60} \)°.
5. Combine the values to express the angle in decimal degrees.

Key Concepts

Degrees and Minutes

In trigonometry, angles can be measured in degrees, where one full rotation is 360 degrees. Each degree can be further divided into minutes, with one degree equaling 60 minutes. This notation is often used in navigation and astronomy, allowing for more precise angle measurements.

Conversion to Decimal Degrees

To convert an angle from degrees and minutes to decimal degrees, you divide the minutes by 60 and add this value to the degrees. For example, to convert 70° 48', you calculate 48/60, which equals 0.8, and then add it to 70, resulting in 70.8 degrees.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy. In this context, rounding to the nearest thousandth means keeping three decimal places. For instance, if the result of a conversion is 70.8004, it would be rounded to 70.800, ensuring clarity and precision in the final answer.