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`implies b =2xx0.638xx10^(7)=1.276xx10^(7)`m
Angle subtended at moon `theta1^(@)54. = 1.9^(0)`
`implies theta=1.9xx1.745xx10^(-2)= 3.32xx10^(-2) `rad
Distance of moon ,
`D=(b)/(theta)implies D= (1.276xx10^(7))/(3.32xx10^(-2))= 3.84xx10^(8)` m