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From two diametrically opposite points A...

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.

Text Solution

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Distance between points of observation =Diameter of earth i.e
`b=2rArr b=2xx0.638xx10^(7)=1.276xx10^(7)m `, Angle subtented at moon `theta=1^(@)54.=1.9^(@)`
`rArr0=1.9xx1.745xx10^(-2)=3.32xx10^(-2)rad`
Distance of moon,`D=b/(theta)rArrD=(1.276xx10^(7))/(3.32xx10^(-2))=3.84xx10^(8)`
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