From two diametrically opposite points A and B on earth, moon is observed. The angle thetasubtended 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.

From two diametrically opposite points A and B on earth, moon is obser

1.	From two diametrically opposite points A and B on earth, moon is observed. The angle thetasubtended 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.
Answer» Solution :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^(@)` `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