You can put this solution on YOUR website! the rod is point straight up and is perpendicular to the ground.
the shadow is horizontal on the ground,
the ratio of the length of the rod to the shadow is .
this means that for every 1 unit of length of the rod, the shadow is units in length.
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let A be the top of the rod.
let B be the bottom of the rod.
let C be the end of the shadow.
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this forms a right triangle ABC where AB is equivalent to the length of the rod and BC is equivalent to the length of the shadow.
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assume the length of the rod is 1.
this means the length of the shadow is
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angle ACB is the angle that the shadow makes with the top of the rod.
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side AC is the hypotenuse of triangle ABC and if you extend it indefinitely it will intersect with the sun.
the tangent to angle ACB is opposite side / adjacent side = AB / BC which equals 1 / sqrt(3).
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this makes tan (ACB) = 1/sqrt(3) = 1.732050808 which makes angle (ACB) = 60 degrees.
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the 60 degrees represents the attitude of the sun which is the angle that the sun makes with the point of observation on the earth.
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the poiont of observation on the earth is point C of triangle ABC which is the end of the shadow formed from the vertical pole.
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a picture of this can be seen at problem 209226 on the following website:
http://theo.x10hosting.com/
if it's not there, give it a half hour and try again.
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