SOLUTION: A tree growing on a hillside casts a 200-foot shadow. If the hillside is 20 degrees below the horizontal and the angle of elevation to the sun is 80 degrees. How tall is the tree?
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Question 1154884: A tree growing on a hillside casts a 200-foot shadow. If the hillside is 20 degrees below the horizontal and the angle of elevation to the sun is 80 degrees. How tall is the tree? Answer by greenestamps(13200) (Show Source):
With the angle of elevation to the sun 80 degrees and the slope of the hill 20 degrees, the tree, its shadow, and the ray of light from the top of the tree to the tip of the shadow form a triangle with angles of 10 degrees, 60 degrees, and 110 degrees.
The 200-foot shadow is opposite the 10-degree angle; the tree of unknown height is opposite the 60-degree angle.
Use the law of sines.
That is assuming the shadow is directly downhill from the tree. There is no tree in the world that is anywhere near that tall.
The 200-foot shadow could be up the hill; but that would require the tree to be even taller.
