Math is Hard (I need help)

July 22, 2012 3:49 PM

Math is hard. Please help me with a slope-related problem.

I have a project that is 103 inches high on one end, and 119 inches high on the other end. It is 394 inches long.

Given this information, I need an on-line calculator that can tell me the height of a vertical line drawn at any point along the 394 inch length.

PS: I know this is probably simple math, but I'm utterly failing at this for hours and hours. If I have to do the actual math problem I will, but I feel at this point that some kind of automatic calculator is going to be the best solution to get me the right answers, especially since I'm going to need to calculate 20 (or more) vertical lines along this distance.

Thank you!

posted by anastasiav to grab bag (11 answers total)

Can you confirm if the 394 inches is the length of the base (eg, on the floor from one end to the other) or the length of the slope (from the top of one end to the top of the other)?
posted by jeather at 3:54 PM on July 22, 2012 [1 favorite]

(.040609*(distance from the short side in inches))+103 = height of line from that point, in inches
posted by milqman at 4:00 PM on July 22, 2012

slope = rise / run = 16 / 394 = 0.040609137

The height at an place along the length = 103 + (length * 0.040609137)

For instance, the height at the mid point =
103 + (197 * 0.040609137) = 103 + 8 = 111 inches

On preview: I'm assuming that 394 is the horizontal length, not the length of the slope.
posted by Bruce H. at 4:00 PM on July 22, 2012 [1 favorite]

If you have to calculate the height 20 times or so, it might be easiest to use a spreadsheet.
posted by dd42 at 4:04 PM on July 22, 2012

jeather's question is insigthful, but the difference is very small at such a low angle.

If 394 is the length of the slope, the horizontal length is 393.675 inches and the slope is 0.040642663, so the maximum error would be less than 0.014 inches.
posted by Bruce H. at 4:15 PM on July 22, 2012

I'm imagining your project as something like a table or the side view of a table. Your question is ambiguous as to whether the 394 is the length of the table top or the distance between the legs. Bruce H is right that the difference is negligible, but you may want a rundown of the different approaches depending on how you're determining where to make the vertical lines.

(1) If 394 inches is the length along the top:
(a) To plop down the vertical lines from points along the table top,: h = [(16 * d) / 394] + 103, where h is the height of the vertical line, and d is the distance along the "table top" starting from the end that has a corner with the short leg.

(b) To make your vertical measurements based on intervals between the legs, the distance between the legs is ~393.67 by the Pythagorean Theorem, and h = [(16 * d) / 393.67] + 103, where d is a distance along the line along the floor connecting the legs starting at the shorter leg.

(2) If 394 inches is the distance between the legs:
(a) To plop down vertical lines from points along the table top, the length of the table top is ~394.32 inches by the Pythagorean Theorem, and h = [(16 * d) / 394.32] + 103, where d is a distance measured along the table top from its corner with the short leg.

(b) To draw a line going UP from different points along a line connecting the legs, h = [(16 * d) / 394] + 103, where d is a distance along the line along the floor connecting the two legs, starting from the shorter leg.
posted by alphanerd at 4:20 PM on July 22, 2012

Another approach, requiring less computation, would be to divide the length into 16 equal parts of 24.625 inches and add one inch of height at each interval. 24.625 is 24 and 5/8 inches, so measuring to thousandths of an inch would not be required.
posted by Bruce H. at 4:20 PM on July 22, 2012

I made you a Google docs spreadsheet. There's a gigantic table at the bottom with the heights at one-inch intervals.

Or if you want to calculate the height at a fractional distance, you can enter a specific distance in cell B6, and B7 will update with the height at that point. Sadly, to edit the spreadsheet at all, you'll need either sign into google docs and make a copy of the spreadsheet, (which I think is File > Make a copy) or else download it as an Excel file to modify on your own computer.

My math assumes that 394 is the distance between the "legs" (or whatever), not the length of the slope.
posted by jcreigh at 4:23 PM on July 22, 2012

I made you a Geogebra worksheet. Here is the worksheet. Here is Geogebra.

Move (using the Move tool) around the point labeled 'E' and pay attention to the coordinates of E. Since you didn't draw a picture, I assumed this was the orientation. Hope it helps!
posted by oceanjesse at 4:28 PM on July 22, 2012

Thank you for all the answers. I have to confess my eyes glazed over at a lot of them, but jcreigh provided exactly the right tool to make all the pieces fit. Thank you so much!!
posted by anastasiav at 4:35 PM on July 22, 2012

Let me make one attempt to unglaze you, so you have a fighting chance of understanding what the spreadsheet is actually doing for you.

First thing is to draw an imaginary horizontal line right across the project at the 103 inch height. So you now have a long skinny triangle, 394 inches long and 16 inches high, sitting on top of a 394-by-103 inch rectangle. Yes?

So the heights you want are all just 103 inches (the height of the bottom part) plus whatever height the triangular top part adds at the horizontal distance you're interested in.

At the thin end of the triangle it has no height at all. At the thick end it's 16 inches. Half way in between, it's half of 16 inches or 8 inches. 3/4 of the way toward the thick end it's 3/4 of 16 inches or 12 inches.

So you can get the height of the triangle at any point at all, by working out what fraction of the 394-inch width that point is at (that is, divide the horizontal position of the point by 394 inches), then multiplying the result by 16 inches. Having done that, you then add on the 103-inch base height to calculate the total. This is pretty much exactly what the formulas in jcreigh's spreadsheet are doing.

For example: if you wanted the height at the 72-inch mark, you'd do (72 inches ÷ 394 inches) × 16 inches + 103 inches and get 105.9 inches.

All the answers involving a factor of 16 / 394 = 0.040609137 also work by the same logic, since multiplying by (16 / 394) has exactly the same effect as dividing by 394 and then multiplying by 16.
posted by flabdablet at 3:49 AM on July 23, 2012 [1 favorite]