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Convert the following sexagesimal measures of angles in decimal form

To convert the angle \( 84^\circ 35' 25'' \) from sexagesimal (degrees, minutes, seconds) to decimal degrees, we'll use the following conversion:

- 1 minute = \( \frac{1}{60} \) degrees
- 1 second = \( \frac{1}{3600} \) degrees

Now, let's calculate the decimal form:

\[
\text{Decimal Degrees} = 84^\circ + \frac{35'}{60} + \frac{25''}{3600}
\]

I'll compute this now.The angle \( 84^\circ 35' 25'' \) in decimal form is approximately \( 84.5903^\circ \).

Do you have any further questions, or would you like more details on this process? Here are some related questions:

1. How do you convert decimal degrees back into degrees, minutes, and seconds?
2. Can you explain why there are 3600 seconds in one degree?
3. What is the advantage of using decimal degrees over sexagesimal form?
4. How can this conversion be used in navigation or mapping?
5. Could we use a similar method to convert time from hours, minutes, and seconds to decimal form?

**Tip:** When converting angles, always ensure your calculator or tools are set to the correct unit (degrees or radians) to avoid errors.

Convert the following sexagesimal measures of angles in decimal form: 84°35'25"

Learn how to convert the sexagesimal angle 84°35'25" into decimal degrees. The formula used involves dividing minutes and seconds by 60 and 3600, respectively, resulting in an approximate value of 84.5903°. Suitable for students in Grades 9-12.

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