Question 1024306: Hi beloved tutors, can you help me on this question? Thankss
Paul put some rectangular paintings on the wall. For each picture, he put one nail into the wall 2.5m above the floor, and attached a 2m long string at the two upper corners. Which of the following pictures is closest to the floor (format: width in cm × height in cm)?
(A) 60 × 40 (B) 120 × 50 (C) 120 × 90 (D) 160 × 60 (E) 160 × 100
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 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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