The moon is observed from two diametrically opposite points 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 be about `1.276xx10^(7) m`, compute 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 = (1.276 xx 10^(7))/(3.32 xx 10^(-2)) = 3.84 xx 10^(8) m`.