Final answer:
The departures and latitudes are as mentioned above, the linear misclosure is 1685.09 feet, and the relative precision is 1.
Step-by-step explanation:
To compute the departures and latitudes, linear misclosure, and relative precision for the traverse problem 10.6, we need to calculate the individual departure and latitude values for each side of the traverse.
Given the lengths of the sides of the traverse:
ab = 202.74 feet
bc = 283.87 feet
cd = 498.37 feet
de = 320.33 feet
ea = 380.78 feet
1. Departures:
The departure of a side is the horizontal distance between the starting and ending points.
- Departure of ab = ab = 202.74 feet
- Departure of bc = bc = 283.87 feet
- Departure of cd = cd = 498.37 feet
- Departure of de = de = 320.33 feet
- Departure of ea = ea = 380.78 feet
2. Latitudes:
The latitude of a side is the vertical distance between the starting and ending points.
- Latitude of ab = 0 feet (since it is a horizontal side)
- Latitude of bc = 0 feet (since it is a horizontal side)
- Latitude of cd = 0 feet (since it is a horizontal side)
- Latitude of de = 0 feet (since it is a horizontal side)
- Latitude of ea = 0 feet (since it is a horizontal side)
3. Linear Misclosure:
The linear misclosure is the algebraic sum of the departures, which should ideally be zero for a closed traverse.
Linear Misclosure = departure of ab + departure of bc + departure of cd + departure of de + departure of ea
Linear Misclosure = 202.74 + 283.87 + 498.37 + 320.33 + 380.78
Linear Misclosure = 1685.09 feet
4. Relative Precision:
The relative precision of the traverse can be calculated by dividing the linear misclosure by the perimeter of the traverse.
Perimeter of the traverse = ab + bc + cd + de + ea
Perimeter of the traverse = 202.74 + 283.87 + 498.37 + 320.33 + 380.78
Perimeter of the traverse = 1685.09 feet
Relative Precision = Linear Misclosure / Perimeter of the traverse
Relative Precision = 1685.09 / 1685.09
Relative Precision = 1
Therefore, for the given traverse problem 10.6, the departures and latitudes are as mentioned above, the linear misclosure is 1685.09 feet, and the relative precision is 1.