Takahashi has a water bottle with the shape of a rectangular prism whose base is a square of side a cm
and whose height is b cm
. (The thickness of the bottle can be ignored.)
We will pour x cm3
of water into the bottle, and gradually tilt the bottle around one of the sides of the base.
When will the water be spilled? More formally, find the maximum angle in which we can tilt the bottle without spilling any water.
All values in input are integers.
Input is given from Standard Input in the following format:
a b x
Print the maximum angle in which we can tilt the bottle without spilling any water, in degrees. Your output will be judged as correct when the absolute or relative error from the judge’s output is at most 10−6
Sample Input 1
2 2 4
Sample Output 1
This bottle has a cubic shape, and it is half-full. The water gets spilled when we tilt the bottle more than 45
Sample Input 2
12 21 10
Sample Output 2
This bottle is almost empty. When the water gets spilled, the bottle is nearly horizontal.
Sample Input 3
3 1 8
Sample Output 3
This bottle is almost full. When the water gets spilled, the bottle is still nearly vertical.
I need help with this question and if someone helps with the diagram and proof, that will be more helpful.
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