Convert the following angle to decimal degrees.
a= -62  degrees 28' 59"

To convert the angle \(a = -62^\circ 28' 59''\) to decimal degrees, we need to convert the minutes (\( '\)) and seconds (\( ''\)) into a fraction of a degree. Here's how it's done step-by-step:

1. **Convert seconds to minutes:**

\[
59'' = \frac{59}{60} \, \text{minutes}
\]

2. **Convert minutes (including converted seconds) to degrees:**

\[
28' 59'' = 28 + \frac{59}{60} \, \text{minutes}
\]

\[
= 28 + 0.98333 \, \text{minutes} \approx 28.98333 \, \text{minutes}
\]

\[
28.98333' = \frac{28.98333}{60} \, \text{degrees}
\]

\[
= 0.4830555 \, \text{degrees}
\]

3. **Add this to the whole degrees:**

\[
-62^\circ 28' 59'' = -62 + 0.4830555
\]

\[
= -61.5169444^\circ
\]

**Conclusion:**

The angle \(a = -62^\circ 28' 59''\) in decimal degrees is approximately:

\[
a \approx -62.483056^\circ
\]

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

### Related Questions:

1. How do you convert radians to degrees?
2. What is the difference between degrees, minutes, and seconds?
3. How can you convert decimal degrees to degrees, minutes, and seconds?
4. What are some common uses of angles in navigation?
5. How do you use trigonometric functions with angles in decimal degrees?

### Tip:

When converting angles, always remember to maintain the sign (positive or negative) throughout the conversion to avoid any errors in calculations.

Learn how to convert the angle -62 degrees 28 minutes 59 seconds to decimal degrees with a step-by-step explanation. This problem covers converting angles from degrees, minutes, and seconds to decimal degrees. Suitable for high school students and anyone interested in mathematical conversions of angles.

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