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particle decay and zenith angle watch

1. Use the cosine rule to derive a general formula for the propagation distance from the neutrino production height(above the level of the detector). Show that to a good approximation the formulae and for the propagation distance, are good in the 2 case and (R= radius of the earth, H=height above detector)

I drew a diagram and tried to do the first part but got:

which just looks wrong...
2. (Original post by EmmaK90)
Use the cosine rule to derive a general formula for the propagation distance from the neutrino production height(above the level of the detector). Show that to a good approximation the formulae and for the propagation distance, are good in the 2 case and (R= radius of the earth, H=height above detector)

I drew a diagram and tried to do the first part but got:

which just looks wrong...
Case 1 is simply small angle approximation. As is small compared to .
The the Earth will have curved away very little from the point where h is compared to a flat Earth. Thus you just apply cosine = opposite / hypotenius. Simples.

Your second equation seems wrong, since there is no dependance on h...

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