Convert the following angle to decimal degrees. 

a=-81 degrees 31' 17"

To convert the angle \(a = -81^\circ 31' 17''\) to decimal degrees, we'll need to convert both the minutes (\( '\)) and seconds (\( ''\)) into a fraction of a degree. Here are the steps:

1. **Convert seconds to minutes:**

\[
17'' = \frac{17}{60} \, \text{minutes} \approx 0.28333' 
\]

2. **Add this to the minutes to get the total minutes as a decimal:**

\[
31' + 0.28333' = 31.28333'
\]

3. **Convert the total minutes to degrees:**

\[
31.28333' = \frac{31.28333}{60} \, \text{degrees} \approx 0.5213883^\circ
\]

4. **Add this to the whole degrees (keeping the negative sign):**

\[
a = -81^\circ + 0.5213883^\circ = -81.5213883^\circ
\]

**Conclusion:**

The angle \(a = -81^\circ 31' 17''\) in decimal degrees is approximately:

\[
a \approx -81.5214^\circ
\]

### Would you like more details or have any questions?

### Related Questions:

1. How do you convert decimal degrees back to degrees, minutes, and seconds?
2. What are some applications of using angles in decimal degrees?
3. How can you convert degrees to radians?
4. What is the significance of the negative sign in angle measurements?
5. How are angles measured differently in different coordinate systems?

### Tip:

When converting minutes and seconds to decimal form, remember that there are 60 minutes in a degree and 60 seconds in a minute. This is key for accurate conversions!

Learn how to convert the angle -81 degrees 31 minutes 17 seconds to decimal degrees. This problem involves converting degrees, minutes, and seconds to decimal form, essential for precise angular measurements. Suitable for high school students studying trigonometry and angular conversions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation