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 = 2 xx 0.638 xx 10^7 = 1.276 xx 10^7`m , Angle subtended at moon `theta = 1^@ 54. = 1.9^@`
`implies theta = 1.9 xx 1.745 xx 10^(-2) = 3.32 xx 10^(-2)` rad
Distance of moon, `D = b/theta implies D = (1.276xx10^7)/(3.32xx 10^(-2)) = 3.84 xx 10^8` m