An EDM slope distance AB is determined to be 561.276 m. The EDM instrument is 1.820 mabove station A, and the prism is 1.986 m above station B. The EDM instrument is mounted ona theodolite whose optical center is 1.720 m above the station. The theodolite was used tomeasure the vertical angle (+6°21’38’’) to a target on the prism pole; the target is 1.810 mabove station B. With help of a diagram compute both the horizontal distance AB and theelevation of Station B, if the elevation of station A=186.275
Question
An EDM slope distance AB is determined to be 561.276 m. The EDM instrument is 1.820 mabove station A, and the prism is 1.986 m above station B. The EDM instrument is mounted ona theodolite whose optical center is 1.720 m above the station. The theodolite was used tomeasure the vertical angle (+6°21’38’’) to a target on the prism pole; the target is 1.810 mabove station B. With help of a diagram compute both the horizontal distance AB and theelevation of Station B, if the elevation of station A=186.275
Solution
To solve this problem, we need to use trigonometry and the concept of slope distance.
Step 1: Calculate the difference in height between the EDM instrument and the target on the prism pole.
The height of the EDM instrument above station A is 1.820 m and the height of the target on the prism pole above station B is 1.810 m. So, the difference in height is 1.820 m - 1.810 m = 0.010 m.
Step 2: Calculate the slope distance from the EDM instrument to the target on the prism pole.
The slope distance AB is given as 561.276 m. But this is the distance from the EDM instrument to the prism, not the target on the prism pole. So, we need to subtract the difference in height calculated in step 1 from the slope distance.
So, the slope distance from the EDM instrument to the target on the prism pole is 561.276 m - 0.010 m = 561.266 m.
Step 3: Calculate the horizontal distance AB.
The horizontal distance can be calculated using the formula:
Horizontal distance = Slope distance * cos(vertical angle)
The vertical angle is given as +6°21’38’’. Convert this to decimal degrees by dividing the minutes by 60 and the seconds by 3600, then adding the results to the degrees. So, 6°21’38’’ = 6 + 21/60 + 38/3600 = 6.36056 degrees.
So, the horizontal distance AB = 561.266 m * cos(6.36056) = 558.999 m (approximately).
Step 4: Calculate the elevation of station B.
The elevation of station B can be calculated using the formula:
Elevation of B = Elevation of A + Slope distance * sin(vertical angle) - Height of prism above station B
So, the elevation of B = 186.275 m + 561.266 m * sin(6.36056) - 1.986 m = 227.256 m (approximately).
So, the horizontal distance AB is approximately 558.999 m and the elevation of station B is approximately 227.256 m.
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