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Question 208201: What is the fall (drop) in inches if a line drops 1 degree every 100 feet ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! that should be a right triangle with the altitude equal to the drop every 100 feet.
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let A be your starting point.
let B be 100 feet away in a horizontal direction.
let C be where the line has dropped after 100 feet in a vertical direction.
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you have a right triangle ABC, where B is the right angle.
your angle A is 1 degrees.
the side opposite to your angle A is BC which is the vertical drop.
the side adjacent to your angle A is AB which is 100 feet long.
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you want to find the length of BC
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the length of BC can be found by the formula:
tan (A) = tan (1 degree) = opposite / adjacent = BC / AB = BC / 100
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your formula is:
tan (1 degree) = BC / 100
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tan (1 degree) = .017455065
formula becomes:
.017455065 = BC / 100
multiply both sides by 100 to get:
.017455065 * 100 = BC
BC = 1.745506495 feet
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BC in inches would be 1.745506495 * 12 = 20.94607791 inches.
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this is approximate because the line doesn't perfectly match a straight line when it drops. there's a bit of a curve to it much like what you see on telephgone or electrical cables between telephone poles, so the real answer would be much more complicated for what i think they are asking you to do and would probably involve the calculation of an arc or a small section of a very large circle or ellipse.
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use of a right triangle concept gets you close to the real answer and hopefully is what they are asking you to do.
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