Question

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the moon is observed from two diametrically opposite point A and B on earth.the angle theta subtended at the moon by the two directions of observation is 1°54' .given the diameter of the earth to the earth to be about 1.276×10^7 m. compute the distance of the moon from the earth.

Answer 1

ø=1°54'=114'=(114×60)"=114×60×4.85×10^-6 rad = 3.32×10^-2 rad
Basis, b=AB=1.276×10^7 m
So, the distance of the moon from the earth,
S= b/ø =(1.276×10^7)÷(3.32×10-2)= 3.84×10^8 (ans)

Answer 2

The moon is observed from two diametrically opposite points A and B on earth. The angle subtended at the moon by two directions of observation is 1∘54′. The diameter of the earth is 1. 276×107m .