Spherical Trigonometry? Help!!!

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Old Dec 12, 2005 | 12:04 PM
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Question Spherical Trigonometry? Help!!!

Anyone know anything about Spherical Trigonometry? Hep me...Hep me...

I have NO CLUE how to solve this puzzle, but would REALLY like to get to this Geocache...
Originally Posted by geocaching.com
“Now when Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, saying, where is he that is born King of the Jews? For we have seen his star in the east, and are come to worship him… and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was. When they saw the star, they rejoiced with exceeding great joy.”
-Matthew, apostle of Jesus the Christ, AD 50
A brisk December evening found an old man gazing westward into the afterglow of a sunset whose glory had passed. The brilliant orange and pink had given way to darker hues as night drew closer.

A sparkling point of light caught his eye as it pierced the deep blue twilight.

The silence of this newborn night awoke his idle musing,
“The first star of night this must be, yet how bright it is! Perhaps this is the Evening Star herself, Venus, as the Romans call her, weaving her way through the lattice of lesser stars in an intricate dance with the Sun. Sometimes running ahead of him, at others she lingers behind to watch as the world beneath is bathed in the darkness her Sun has left behind...”
Lost in thought, he watched as the night sky blossomed into a shimmering garden of countless stars. Like the lights of a thousand ships adrift on the streams of a great black sea, the stars drifted along in unison toward the western horizon. His gaze kept returning to that first bright star, still high in the western sky.
The realization struck suddenly, startling him from his reverie: the star was still high in the western sky; it did not appear to have moved at all. Scanning the sky for evidence of this astronomical impossibility, it was but moments before he found it. The constellation Orion lie just above the western horizon, below the hanging star in the west; yet he was sure he had watched the constellation appear from the darkening twilight above and well to the east of the new star.
“Surely, this must be a Sign, but what could it mean?” His thoughts racing, he hurried to his study. Trembling with excitement, he gathered a few instruments and carefully made his way up the dark, winding stair of his observation tower. Emerging from the darkness of the stair, the gentle brilliance of a thousand stars burst upon him, but his eyes came to rest on only One, well above the western horizon. Securing the sextant, he kept his eyes fixed on this new Star while his hands meticulously worked the familiar dials, and in a few moments the Star was perfectly sighted in. Turning to an empty page in the record book, he took took up the pen and carefully recorded these coordinates:

Azimuth: 272 degrees, 12 minutes, 32 seconds
Elevation: 59 degrees, 20 minutes, 37 seconds

He dared not look away or even blink for some minutes, and yet the star did not move at all. “What could be the meaning of this new Wonder? Why should the Star first appear tonight? What is the significance of that single point in the sky, that this new Star will not drift from it?” A torrent of questions flooded his mind, begging to be answered, but not a single answer could be offered. He glanced down at the record book and idly wondered if his colleagues were in their towers tonight, all recording the same coordinates. He dismissed the thought, even as it emerged. “As with any star,” he reasoned to himself, “each of my colleagues will be recording a different set of coordinates, depending on their unique horizon provided by the curvature of the earth.”
In a sudden revelation, the puzzle unfolded before him, “If this new Star is fixed at a single point in the sky, then it follows that there must be one precise location on the Earth that lies directly beneath the Star. Furthermore, given the azimuth and elevation of the Star as seen from a known observation point, that location could be mathematically determined!” Thumbing his way through the record book, he discovered the inscription he sought on the inside of the back cover:

Observation Tower
49 degrees, 22 minutes, and 27 seconds from the North Celestial Pole
75 degrees, 22 minutes, and 15 seconds west of the Prime Meridian

There awoke in the old man a childlike excitement. He knew that tomorrow there would be great speculation and deliberation on the new Star. They would determine what point the star was over and perhaps they would even deduce what lie at the foot of the Star. Yet he trembled with a deeper thrill, for somehow he knew that this would not end with debate and discussion. He must prepare for a long journey; he must follow this new Star.
I'm guessing that by using spherical trig, one is able to garner a latitude and longitude from the figures given...

Can you resident Brainiacs help a brotha out?!!!
 
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Old Dec 12, 2005 | 02:17 PM
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Dang... Where's Kobi when ya need him?!!
 
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Old Dec 12, 2005 | 02:39 PM
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I can probably help you out......using "regular" geometry....give me a few...
 
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Old Dec 12, 2005 | 02:52 PM
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From: ???.....depends on the day
do you have an "approximate" location that this is? (i.e. city, state).....do you have the registered "cache number" from www.geocaching.com ?
 
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Old Dec 12, 2005 | 03:30 PM
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Originally Posted by wstahlm80
do you have an "approximate" location that this is? (i.e. city, state).....do you have the registered "cache number" from www.geocaching.com ?
Yeah, it's outside of Kingman, AZ... In the Hualapai Mountains...

Waypoint is GCRJY0

I wish I knew someone that's a surveyor by trade...

TIA Bill...
 
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Old Dec 12, 2005 | 04:32 PM
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Originally Posted by BRUZRs_Daddy
Yeah, it's outside of Kingman, AZ... In the Hualapai Mountains...

Waypoint is GCRJY0

I wish I knew someone that's a surveyor by trade...

TIA Bill...

Thanks BRUZR:

Things are picking up at work...so I will try to get this thing done tonight....looks like a GREAT cache to do....hopefully there is some nice scenery and trails on your way there....If I get this thing figured out and it is right, I will mail you something to place in that cache as well...in fact, I have a Travel BUG that I can send you.....it is really not a "Christmas-themed" item.....but it is a BUG none the less....
 
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Old Dec 12, 2005 | 04:40 PM
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Originally Posted by wstahlm80
Thanks BRUZR:

Things are picking up at work...so I will try to get this thing done tonight....looks like a GREAT cache to do....hopefully there is some nice scenery and trails on your way there....If I get this thing figured out and it is right, I will mail you something to place in that cache as well...in fact, I have a Travel BUG that I can send you.....it is really not a "Christmas-themed" item.....but it is a BUG none the less....
Cool, How do you want me to send you my address?
 
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Old Dec 12, 2005 | 04:48 PM
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Originally Posted by BRUZRs_Daddy
Cool, How do you want me to send you my address?

Let me make sure that I get the problem correct first....the guy/girl that created the cache will let other cachers email him/her to make sure that the coordinates that are calculated are the correct coodinates...

....I have never attempted a problem like this before....but I have done similar calculus problems....so combining that with some survey knowledge....I think that I can get an answer.....

...I will shoot you an email when I do and we can go from there.....
 
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Old Dec 12, 2005 | 05:04 PM
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Right on!!!
 
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Old Dec 13, 2005 | 10:45 AM
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Billy Boy... Any luck?
 
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Old Dec 13, 2005 | 10:50 AM
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Originally Posted by BRUZRs_Daddy
Billy Boy... Any luck?

Nope.....I forgot all my materials I printed out here at the office...so I was not able to work on it...I have placed them next to my keys...so I hope to not forget them today.... :o
 
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Old Dec 13, 2005 | 11:05 AM
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Sucka!!!

No really, it's cool. It's like an hour away, so I won't likely get to try until this weekend anyway...
 
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Old Dec 19, 2005 | 09:49 AM
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OK Bill, I skipped this one this weekend and went out for another puzzler...

Still no goodie? I give you props no matter what!!! When I looked at that and went to the page on spherical trig, I just started feeling really stoopid and started to drool...
 
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Old Dec 19, 2005 | 09:58 AM
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Originally Posted by BRUZRs_Daddy
OK Bill, I skipped this one this weekend and went out for another puzzler...

Still no goodie? I give you props no matter what!!! When I looked at that and went to the page on spherical trig, I just started feeling really stoopid and started to drool...

Well....I didn't have time to work on it this weekend...I went pheasant hunting instead....but this problem has definitely sparked my curiousity....I will complete this for you....just might take some time...
 
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Old Dec 19, 2005 | 10:00 AM
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Originally Posted by wstahlm80
Well....I didn't have time to work on it this weekend...I went pheasant hunting instead....but this problem has definitely sparked my curiousity....I will complete this for you....just might take some time...
RIGHT ON, Mang!!!
 
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