From two diametrically opposite points A and B on earth, moon is observed. The angle `theta` subtended at the moon by the two directions of observation is `1^@ 54^1`. If radius of earth is` 0.638 xx 10^7` m, find the distance of the moon from the earth.

Explanation

Distance between points of observation = Diameter of earth
i.e., `b=2r rArr b=2 xx 0.638 xx 10^(7) = 1.276 xx 10^(7)` m
Angle subtended at moon `theta= 1^(@) 54. = 1.9^(@)`
`rArr theta = 1.9 xx 1.745 xx 10^(-2) = 3.32 xx 10^(-2)` rad Distance of moon,
`D= (b)/(theta) rArr D = (1.276 xx 10^(7) )/( 3.32 xx 10^(-2) )= 3.84 xx 10^(8)` m