Question: User: 18. (3 points) Find the back azimuths of the direction 326°00'31".
a. 90°00'31"
b. 146°12'29"
c. 194°45'06"
d. 50°00'31"
e. None of the above
19. (3 points) Compute the bearings of Line SW using the figure below.
a. S 41°24'56" W
b. S 61°57'43" W
c. S 48°35'04" W
d. S 70°45'36" W
e. None of the above
Graph position_hint=bottom-right: A compass-style azimuth/bearing diagram centered at S, with rays to X in the northwest labeled N 17°16'41" W, to T in the northeast labeled 77°49'27", to U in the southeast labeled S 65°47'03" E, to V in the southwest, and to W in the west-southwest; arc labels include 61°57'43", 41°24'56", and 93°07'43".
1. **Problem 18: Find the back azimuth of the direction $326^\circ00'31''$.**
2. **Definition:** The back azimuth is the direction opposite to the given azimuth. To find it:
- If the azimuth is less than $180^\circ$, add $180^\circ$.
- If the azimuth is $180^\circ$ or more, subtract $180^\circ$.
3. Given azimuth: $326^\circ00'31''$ which is greater than $180^\circ$.
4. Calculate back azimuth:
$$326^\circ00'31'' - 180^\circ = 146^\circ00'31''$$
5. Compare with options:
- Option b is $146^\circ12'29''$, close but not exact.
- None of the other options match.
6. Since none exactly match, answer is **e. None of the above**.
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7. **Problem 19: Compute the bearing of Line SW using the figure.**
8. From the description, the arc labels include $61^\circ57'43''$, $41^\circ24'56''$, and $93^\circ07'43''$.
9. Bearings are given as S (angle) W.
10. The bearing of Line SW corresponds to the arc labeled $61^\circ57'43''$.
11. Therefore, the bearing is:
$$\text{S } 61^\circ57'43'' \text{ W}$$
12. This matches option b.
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**Final answers:**
- Problem 18: e. None of the above
- Problem 19: b. S 61°57'43" W