Question

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

Answer 1

Here parallactic angle, 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)