Question

You cut a circular hole 1/4-inch in diameter in a piece of cardboard . With the cardboard 30 in. from your face, the moon fits exactly into the hole. The moon is about 240,000 miles from Earth. Is the moon more than 1,500 miles?

Answer 1

I feel like this question is a bit weird since it didn't include the form of the triangle formed from the eye to the hole there are two options:



either way, the procedure would be the same just set a proportion between the two triangles you get the one from the image above and another imaginary triangle from eye straight to the moon without the piece of paper:

\(\boxed{\frac{\text { Earth-Moon distance }}{\text { cardboard distance }} = \frac{\text { Moon's diameter }}{\text { square hole }} }\)

Answer 2

\[\frac{ 1 }{ 4 }inch=\frac{ 1 }{ 4\times12\times3\times1760 }~miles\]
\[30~inch=\frac{ 30 }{ 12\times3\times1760 }miles\]

Answer 3

\[\frac{ DC }{ AC }=\frac{ EB }{ AB}\]
\[\frac{ h }{ 240,000 }=\frac{ \frac{ 1 }{ 4\times12\times3\times1760 } }{ \frac{ 30 }{ 12\times3\times1760 }}\]
\[h=\frac{ 1 }{ 4\times12\times3\times1760 }\times \frac{ 12\times3\times1760 }{ 30}\times 240,000=?\]

Answer 4

correction in the diagram
not 24,000 miles
but 240,000 miles

Answer 5

ty!!