Question 1024306
I will show you the formulas necessary to calculate the distance above the floor for each painting.
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each painting is hung with three nails, one is 2.5 meters above the floor and one nail in each top corner of the painting suspended from a 2 m string attached to each nail.  if we center the painting, then each part of the arch is 1 meter or 100 cm in length.
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to calculate the angle t for the arc we note that the radius for the arc is 1/2 the width of the picture.  we will use this to calculate the length of the cord between a nail at a corner and the nail in the wall - we will use this length to calculate the distance d that the picture hangs from the 2.5 m nail.
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the angle t is ( 100cm / (2 * pi * ( (1/2) * width of painting)) ) * 360
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cord length = 2 * ( (1/2) * width of painting ) * sin(t/2)
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d^2 = (cord length)^2 - ( (1/2) * width of painting)^2
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d = square root(cord length)^2 - ( (1/2) * width of painting)^2)
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now the distance above the floor in cm will be
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250 - d - (height of picture)
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note that, in practice, we would not locate the two nails at the top corners of a painting. The two nails would be located some distance from the top of the painting so that the string or wire connecting them does not show.
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