Question

A slope distance of 165.360 m (corrected for meteorological conditions) was mea- sured from A to B, whose elevations were 447.401 and 445.389 m above datum, respectively. Find the horizontal length of line AB if the heights of the EDM instru- ment and reflector were 1.417 and 1.615 m above their respective stations.

Answer 1

The horizontal length of line AB is 165.358 m.

Step-by-step explanation:

The question is asking to find the horizontal length of line AB given the slope distance and the elevations at points A and B. Similarly, the heights of the instruments are provided to correct the measured slope distance to the actual horizontal distance. To find the horizontal length, we will first need to calculate the vertical difference between the two points and then use trigonometry to derive the horizontal distance, accounting for the instrument heights. To find the horizontal length of line AB, we need to use the concept of slope distance and height difference between the stations. Given that the heights of the EDM instrument and reflector were 1.417 and 1.615 m above their respective stations, we can calculate the vertical height difference to be 0.206 m.

Using the Pythagorean theorem, we can find the horizontal length as follows:

Horizontal length = √(slope distance^2 - vertical height difference^2) = √(165.360^2 - 0.206^2) = 165.358 m