"If it flies directly" means that it will fly a great circle route.

Here's the route (London is at the bottom of the image, Los Angeles at the top):

Image from Google Earth.

We learned above that the latitude and longitude for London and Los Angeles are as follows:

London: φ_{1} = 51°32' N = 0.899426,

λ_{1} = 0° 5' W = −0.001454

Los Angeles: φ_{2} = 34° 3' N = 0.594285,

λ_{2} = 118° 14' W = −2.063561

Applying the formula for the central angle gives:

Central angle =

`2 arcsin sqrt( sin^2 ((-0.305)/2) +cos (0.899) cos (0.594) sin^2 ((-2.062)/2) )`

= 1.374296 (full calculator accuracy was used throughout)

So the distance between London and Los Angeles is:

s=rθ= 6371 × 1.374296 = 8756 km

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