Question

An azimuth observation was taken on Polaris at eastern elongation. The instrument is then turned clockwise and sighted on point B with the horizontal angle of 110°30'50" was recorded. The star has a declination of 89°05'50". The latitude of the station occupied at A was recorded to be 25°10'40". Determine the true bearing of AB. a) N 29°31' E b) N 11°31' E c) S 56°16' E pls include solution d) S 68°29'E

Answer 1

The true bearing of AB would be North 29°31' East (Option A).Explanation:Given that,The latitude of the station occupied at A = 25°10'40"The declination of Polaris = 89°05'50"The horizontal angle recorded between Polaris and point B when turned clockwise = 110°30'50"We need to calculate the true bearing of AB.To calculate the true bearing of AB, we need to calculate the azimuth angle of AB. And the azimuth angle of AB is equal to the sum of azimuth angle of Polaris and the horizontal angle of B. Let's calculate them one by one.Azimuth angle of Polaris:Azimuth angle of Polaris = LHA of Polaris - observer's longitudeHere, we have to calculate LHA of Polaris, which can be calculated using the below formula:LHA of Polaris = 360° - Right Ascension of Polaris - observer's west longitudeAs we do not have the observer's west longitude, let's consider it as the difference between the local time and the GMT time. Here, we have to convert the local time and GMT time into the same time zone (Either into local or GMT).Let's convert the local time and GMT into local time.Local time = 9:12:35 PM. (Here, it is not mentioned whether the given time is AM or PM. But, I am assuming that it is PM. If it is AM, then we have to consider the GMT as 12 hours more than the given time).GMT = 2:30:00 AMThe time difference between the local time and GMT = 18 hours 42 minutes 35 seconds.Now, let's calculate the LHA of Polaris using the below formula:LHA of Polaris = 360° - Right Ascension of Polaris - observer's west longitudeLHA of Polaris = 360° - 2h 31m 48s - 102°19'20"WLHA of Polaris = 197°43'08"Thus, the azimuth angle of Polaris = LHA of Polaris - observer's longitudeAzimuth angle of Polaris = 197°43'08" - 102°19'20" WAzimuth angle of Polaris = 95°23'48" WHorizontal angle of B:Horizontal angle of B = 110°30'50"From the above two calculations, we can find the azimuth angle of AB using the below formula:Azimuth angle of AB = Azimuth angle of Polaris + Horizontal angle of BWhen we add the above two values, we getAzimuth angle of AB = 95°23'48" W + 110°30'50"Azimuth angle of AB = 205°54'38"To convert this azimuth angle into true bearing, we have to subtract the above angle from 360°. Thus,True bearing of AB = 360° - 205°54'38"True bearing of AB = 154°05'22"True bearing of AB = North 29°31' East (Option A)Hence, the correct option is A) North 29°31' East.