Question #e2d7d

2 Answers
Dec 23, 2017

See below.

Explanation:

enter image source here

From the diagram we can see that #h# is the perpendicular bisector, and bisects #/_ABC#

#/_ABC= 56'=(14/15)^@#

#/_ABD= (7/15)^@#

We seek distance DB

#AD=3168#

#tan((7/15)^@)=(AD)/(DB)#

#DB=(AD)/(tan((7/15)^@))=3168/(tan(7/15)^@)~~388,947#km

This is the distance to the centres.

The true distance of the Earth from the Moon is 384,400 km. This is close considering the true diameter of the Earth is 12,742 km and not 6336 km.

Dec 24, 2017

enter image source here
Comparing with the available data of radius of the earth I assume that earth's radius #color(blue)(R= 6336" " km# subtends an angle #color(red)(theta =56')# at the center of the moon as shown in above figure. Let #D# be the distance between center of the earth and moon.

#D # being very large we can assume that the length of the earth's radius #R# lye on the arc of a circle drawn taking #D# as radius and moon's center as the center of the circle.

So we can write

#"Arc R"/"Radius D"= theta ("in radian")#

Transforming the angle in radian

#theta=56'=(56/60)^@=56/60xxpi/180#radian

So we get

#R/D= 56/60xxpi/180#

#=>D=(60xx180xxR)/(56pi)=(60xx180xx6336)/(56pi)#km

#=>D~~388956# km

( It is comparable to available figure as shown below)

enter image source here