Assuming the distance of the earth from the moon to be 38,400 km and the angle subtended by the moon at the eye of a person on the earth to be 31, find the diameter of the moon.

Explanation

Let AB be the diameter of the moon and O be the observer.
Given, `angleAOB=31' =31/60xxpi/180rad`
Since the angle subtendedby the moon is very small, itsodiameterwill be approximatelyequal to the small arc of a circle Whose centeris the eye of the observerandthe radius is the distanceof the earthfrom the moon.Also the moon subtendsan angle of 31' at the centerof this circle. Thus,

`theta=l/r`
`:. 31/60xxpi/180=(AB)/384400`
or `AB=31/60xx22/(7xx180)xx384400=3467.74 km`