Bonsoir,
1) OM = OL = 6370
OS = 4880
Par Pythagore dans le triangle OSL rectangle en S,
[tex]OS^2+SL^2=OL^2\\4880^2+SL^2=6370^2\\23814400+SL^2=40576900\\SL^2=40576900-23814400\\SL^2=16762500\\SL=\sqrt{16762500}\\\boxed{SL\approx4094\ km}[/tex]
2) Dans le triangle OSL rectangle en S,
[tex]\cos(\widehat{SOL})=\dfrac{OS}{OL}\\\\\cos(\widehat{SOL})=\dfrac{4880}{6370}\\\\\widehat{SOL}=\cos^{-1}(\dfrac{4880}{6370})\\\\\boxed{\widehat{SOL}\approx40^o}[/tex]
3) [tex]\widehat{SOM}=90^o\\\\\widehat{SOL}\approx40^o\\\\\widehat{LOM}=\widehat{SOM}-\widehat{SOL}\\\\\widehat{LOM}\approx90^o-40^o\\\\\boxed{\widehat{LOM}\approx50^o}[/tex]
