



 
Hi Frank, Here is how I see the situation you describe. Frank is at point F and the vapors cover the triangle FAB. I let C be the midpoint of AB so the distance from F to C is approximately 35,000 feet and you want to find the distance from A to B. Since C is the midpoint of AB the angle ACF is a right angle. Suppose the angle CFA has measure t degrees then
and hence
and
You told us that you used a compass to find the bearings of A and B from F so that will allow you to determine the measure of the angle BFA and half of that is t. I am not sure how accurately you can measure the length of CF and the bearings of A and B. Measurement errors in these quantities will result in inaccuracies in the calculation of AB. For example if you think the length of CF is 35,000 ± 1,000 feet and you think you know t within ± 5^{o} then perform the calculation with CF = 34,000 ft and 36,000 ft and with t varying by ± 5^{o} and see how the resulting value of AB changes. Good luck with this, Harley
 


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