Themoon 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) , compute the distance of the moon from the Earth.

Themoon is observed from two diametrically opposite points A and B on

1.	Themoon 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) , compute the distance of the moon from the Earth.
Answer» SOLUTION :We have `theta = 1^(@)54. =114. = (114xx60)"xx(4.85xx10^(-6))` rad =`3.32xx10^(-2)` rad, Since `1" = 4.85xx10^(-6)` rad, Also b=AB=`1.276xx10^(7)m` Hence from Eq. (2.1.) , we have the earth-moon DISTANCE. D=b/`theta` `=(1.276xx10^(7))/(3.32xx10^(-2))` `=3.84xx10^(8)m`