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BACKGROUND:

On June 28th, 2003 I was aboard my boat in Rosario Strait in Washington
state USA.  I could see Mount Rainier and Mount Baker simultaneously.
These mountains are not often both visible at once due to distance and
weather.  (These mountains have the greatest snowfall of any mountains
measured on earth.  Mount Rainier had 1,122 inches during the winter of
1971-1972 but Mount Baker stole the record during the winter of
1998-1999 with 1,140 inches of snowfall!)

I used a pair of Fujinon 7x50 binoculars with an internal compass to
take bearings of these two great mountains.  I wondered if I could
mathematically determine my position from the information I gathered...

PROBLEM:

Given two bearing measurements of two mountains whose locations
(latitudes and
longitudes) are known, what are the latitude and longitude of the point
where the measurements are taken from?

This problem can be reworded in geometrical terms as determining the
point of intersection of two lines on a sphere.

DATA:

Mount Rainier's 14,410 foot summit is at 46d 51m 10s North, 121d 45m
31s West
Mount Baker's 10,785 foot summit is at 48d 46m 39s North, 121d 48m 43s
West
I sighted Mount Baker at 50 degrees east of North.
I sighted Mount Rainier at 140 degrees east of North.
The compass was uncorrected for magnetic deviation for these readings.
 From http://www.ngdc.noaa.gov/cgi-bin/seg/gmag/fldsnth2.pl the magnetic
deviation for this location and date is 18d 47m East.

CHALLENGE:

Determine the point of observation!

   

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