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^(0)`
`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