A 2.5-km baseline is measured with an electronic total station. If the vendor's accuracy specification of the instrument is ± (5mm + 2ppm), calculate the accuracy of the measured distance to the nearest thousand.

To determine the accuracy of the measured distance using the provided specifications of the electronic total station, we can break down the accuracy calculation step by step.

The accuracy specification provided is ±(5 mm + 2 ppm). This means that the total potential error consists of two components: a fixed component (5 mm) and a variable component based on the length of the baseline measured (2 parts per million).

First, let's calculate the variable component for a 2.5 km baseline:

1. Convert 2.5 km to meters: 2.5 km = 2500 meters.
2. Calculate the 2 ppm component: [ 2 , \text{ppm} \times 2500 , \text{m} = 2 \times \frac{2.5 , \text{m}}{1,000,000} = 0.005 , \text{m} = 5 , \text{mm}. ]

Now, combine the fixed accuracy and the variable accuracy:

• Fixed component: 5 mm
• Variable component: 5 mm (from the 2 ppm calculation)

The total accuracy then becomes: [ \text{Total accuracy