The Moon subtends an angle of `1^(@)` 55' at the base line equal to the diameter of the Earth. What is the distance of the Moon from the Earth? (Radius of the Earth is `6.4 xx 10^(6)` m)

Explanation

Angle `theta = 1^(@) 55.= 115. = (115xx 60).. xx (4.85xx10^(-6))` rad = `3.34 xx 10^(-2)` rad
Since 1" = `4.85 xx 10^(-6)` rad
Radius of the Earth = `6.4 xx 10^(6)` m
From the Figure 1.5 AB is the diameter of the Earth (b) = `2 xx 6.4 xx 10^(6)` m
Distance of the Moon from the Earth x = ?
`x = (b)/(theta) = (2xx6.4xx10^(6))/(3.34xx10^(-2))`
x = `3.83 xx 10^(8)` m