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Question

During a total eclipse of the sun, the moon is directly in line with the sun and blocks the sun rays. The distance DA between the earth and sun is 93,000,000 miles the distance De between earth and the moon is 240,000 miles and the radius AB of the sun is 432, 500miles . Use the diagram and given measurements to estimate the radius EC of the moom. Tound ypur answer to the nearest mile.

Answer 1

If you assume the "tip" of the sun's rays on the earth come to a single point, then two similar triangles are formed like this:

So you can set up a proportional relationship like this:

So, cross multiplying, we get (r_EC)(d_A) = (r_AB)(d_E) then, dividing both sides by d_A, we get:

r_EC = (r_AB)(d_E)/(d_A) then just plug in the numbers.