You cut a square hole 1/4 inch wide in a piece of cardboard. with the cardboard 30 inches from your face, the moon fits exactly into the square hole. the moon is about 240,000 miles from earth. estimate the moon's diameter. draw a diagram of the situation. then write a proportion and solve the problem.

We need to find the angle (theta) formed by a 1/4 inch object (the hole in the cardboard) from your viewpoint 30 inches away.

tangent theta = opposite/adjacent = .25 / 30 = 0.0083333333
arc tangent (0.0083333333)  = 0.47745 Degrees
(This is also the apparent angular size of the Moon.)

We need to know the size of the Moon.
We know it is 240,000 miles distant and it has an angular size of 0.47745 degrees.

From trigonometry we know
tangent (0.47745 degrees) = Moon diameter / 240,000
Moon diameter =  tangent (0.47745 degrees) * 240,000
Moon diameter =  0.0083333 * 240,000
Moon diameter =  1999.99 miles (rounds to 2,000 miles)
So, from our experiment, we have determined that the Moon is about 2,000 miles in diameter.

SOURCE:  I'd seriously suggest you go to this page:
http://www.1728.org/angsize.htm

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