(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An airliner flies from London Heathrow (latitude 51[tex]^{o}[/tex]30' N, longitude 0[tex]^{o}[/tex] 10' W) to Tokyo Narita (latitude 35[tex]^{o}[/tex] 40' N, longitude 139[tex]^{o}[/tex] 45' E). Assuming that the Earth is spherical and the aeroplane takes a great circle route,

a)what is the total distance flown in nautical miles

b)in what direction (bearing E of N) does the pilot set out from Heathrow

c)what is the most northerly location (latitude and longitude) that the plane reaches on its great circle route?

2. Relevant equations

sinA/sina = sinB/sinb = sinC/sinc

cosa=cosb.cosc+sinb.sinc.cosA

3. The attempt at a solution

I have completed parts a) and b) and have found the answers to be 5161 nautical miles and 31.6[tex]^{o}[/tex] respectively.

For part c I have found the latitude to be 70.95[tex]^{o}[/tex] but can't think how to find the longitude as the spherical triangle I have drawn doesn't have enough information and I don't know how to go about finding what I need in order to get the answer.

I have attached a copy of my spherical triangle but it's rather small, my artistic skills are rather limited using a laptop with no mouse...

On my diagram point N is the North Pole, point H is Heathrow and point P is the most northerly point. All of the numerical values given are in degrees. I have another diagram including point T for Tokyo but have omitted this as I don't think it's necessary for the task. If it is please say, and I will upload it.

Thanks in advance!

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# Astronomy - Latitude and Longitude problem

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