# Some interesting question in 3d geometry

first and second turnings of angle x were .5(":18'48" and 1t)1"I'/'4410' and the readings after the first and second turnings of angle Y were 309".-71'06" and 2`58"4 ?.' 10".

Calculate each angle and the horizon misclosure.

1. A zenith angle is measured as 84°13'56" in the direct position. What is the equivalent to zenith angle in the reversed position?

2. What is the average zenith angle given the following direct and reversed readings 9 )irect: 87°45'04", 87"45'12", 87°4S'08" Reversed: 272" 14'SO", 272" 14'49", 272" 14'5"2"

In Figure 8.9(c), direct and reversed directions observed with a total station instrument from A to points 1^{3, C,} and D are listed in Problems 8.23 and 8.24. Determine the values of the three angles and the horizon misclosure.

3. Direct: 01)1'00", 26"29'21 ", 92"57'44", 0"00'04" Reversed: 0°00'(H)", 26"29' 17", 92°57'46", tY'00'02"

4. Direct: 0"(N)'OO", I06°52'06" 11 91 "38'43", 359°59'58" Reversed: 0°00'(H1", 106°52_'04", 19103x'4 f ", (l°(H)'(H)"

5. The angles at ^{point X were meas}u^{r}ed with a total station instrument. Based on h readings, the standard deviation of the angle was _E6.8". 11' the sane procedure is used in measuring each angle within it eight-sided polygon.; what is the estimated standard deviation of closure?

6. The line of sight of a total station is out of adjustment by 12".

(a) In prolonging a line by plunging the telescope between backsight and foresight, but not double centering, what angular error is introduced?

(b) What off-line linear error results on it foresight of 300 m'?

7. A line /'Q is prolonged to point R by double-centering.`i'wo foresight points R' and R" are set. What angular error would be introduced in single plunging based on the following Icngths of QR and R' R", respectively?

(a)` 650.50 ft and 0.35 it.

(b) 3I2.60 m and 42 nom.

8. Explain why the "principal of reversion" is important in angle measurement.

9. What is the index error and how can its value be obtained and eliminated from observed zenith angles'?

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