The experiment:
1: Wait for a clear night with a clear view of the moon.
2: Stand still.
3: Find a friend, a hooker will work if you don't have any friends, and tell him/her to move several hundred miles away from you.
4: Measure the distance between the two of you, and the angle that the moon is from both of you. You will need to measure the angles at the same time. Use a telescope and a protractor to measure the angle if needed.
5: Using the below formulas, calculate the distance between the earth and the moon.
Explanation:
A = your standing point.
B = the hooker's standing point.
a = your angle to the moon.
b = the hooker's angle to the moon.
d = the absolute value of the sum of the distance between A and B.
h = the distance between the earth and the moon.
x tan(a) = h
and
(d - x) tan(b) = h
From the first equation you get: x = h/tan(a)
Plug this into the second equation and you get: (d * h/tan(a)) tan(b) = h
Solve for h:
h = d * ( ( tan(a) * tan(b) ) / ( tan(a) + tan(b) ) )
Using your knowledge of geometry and trigonometry you can successfully calculate the distance between the earth and the moon yourself!!! Have fun experimenting!
http://en.wikipedia.org/wiki/Triangle