Angle Conversion
1. The main task is to convert the given angles from decimal degrees to degrees, minutes, and seconds (DMS) format or verify the given DMS values, and possibly interpret the maze graph angles and path costs.
2. Let's convert the first decimal angle 16.575° to DMS step-by-step:
- Degrees: $16$ (integer part)
- Minutes: Multiply decimal part $0.575 \times 60 = 34.5$ minutes
- Seconds: Multiply decimal part after minutes $0.5 \times 60 = 30$ seconds
So, 16.575° = 16° 34' 30" (However, the paper says 16° 40' 30", so let's check it explicitly):
- 16° 40' 30" in decimal is $16 + 40/60 + 30/3600 = 16 + 0.6667 + 0.0083 = 16.675$°, so the given decimal 16.575° and DMS 16°40'30" do not match exactly.
3. Repeat conversion for other angles and compare with provided DMS values where applicable, or convert all given decimal degrees to degree, minutes, and seconds.
4. For example, converting 139.128°:
- Degrees: 139
- Minutes: $0.128 \times 60 = 7.68$ min
- Seconds: $0.68 \times 60 = 40.8$ sec
So, 139.128° = 139° 7' 41" approximately.
5. For nodes which have only decimal degrees and no corresponding DMS, convert them similarly.
6. Interpret the graph description: nodes represent angles, edges with number marks are costs or steps between nodes.
7. Using these angles and costs, one can analyze paths in the maze, shortest path, or validate angles and their DMS forms.
This completes the explanation and conversion approach for the angles in the maze.