The spacecraft

The spacecraft spotted a radar device at an altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point.
Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a sphere with a radius of 6378km.

Correct answer:

x =  368.3833 km

Step-by-step explanation:

α=34+6037=6034 60+6037=602040+6037=602040+37=60207734.6167   u=615 km R=6378 km β=90+α=90+602077=6090 60+602077=605400+602077=605400+2077=607477124.6167   (x+R)2 = u2 + R2  2 u R   cos α  x=u2+R22 u R cosβR=u2+R22 u R cos124.61666666667° R=6152+637822 615 6378 cos124.61666666667° 6378=6152+637822 615 6378 (0.568083)6378=368.383=368.3833 km



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