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math problem


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#1
Professional Customer

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I'm not much of a math person so I am desperately seeking help. I go out for a walk each day for exercise and there is this hill I plan to walk up someday. It's steep and walking down it is dangerous enough (in the winter time). I'm trying to figure out the angle of the slope. I've done some searching on the Internet but most of the solutions involve stuff I heard of in high school but never really mastered let alone understood (sine, cosine, tangent, etc.). I've attached an image of the elevation taken from my Garmin Forerunner and would appreciate any assistance in finding out the degree of the slope. Thanks in advance.

GArmin Training Centre - Lake Street hill details - what is the degree of elevation.jpg
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#2
Cold Titanium

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Hi,

If I did this correctly the the answer should be approx. 8º

Here's how I got that (I'm not that good at math so don't behead me if I'm wrong)

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#3
GSP Computers

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I came up with the same answer as Cold Titanium. That'll make two of us to be beheaded if I'm wrong.
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#4
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Thanks for your time. In reality the hill looks a lot more like 45 degrees. Also, unless I'm wrong, aren't all the internal angles of a triangle suppose to equal 180 degrees?
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#5
Cold Titanium

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aren't all the internal angles of a triangle suppose to equal 180 degrees?


Yes. In this case it would be 8º+ 82º+ 90º = 180º
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#6
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Thanks again. From your diagram I misinterpreted your 17 as the answer to the question mark for angle C, I got it now. Thanks again. If it's an 8 degree incline why does it look and feel like a 45 degree incline, or did I ask the wrong question originally?

Actually, I've had some time to think about it and am wondering if the 120.42 is actually the hypotenuse. Since I'm being tracked by satellites I don't think the software would be able to calculate the horizontal distance as opposed to the actually distance walked down the hill. Would that make a difference?

Edited by Professional Customer, 17 March 2011 - 02:55 PM.

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#7
6stringer

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No way do I understand this but on the attachment you provided it sure looks like more than 8° to me. But then again, I struggle with helping my teenager with her math so what do I know? :D
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#8
SpywareDr

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It is a hair over 8°:

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:D
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#9
Cold Titanium

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Yeah, I rounded down...
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#10
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I just realized that I can get a graph of the grade for the hill. Does this make sense with the above calculations?

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  • GArmin Training Centre - Lake Street hill details - what is the degree of elevation 2.jpg

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#11
SpywareDr

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Almost 7°:

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#12
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After countless web searches I finally found the answer using the two websites below. The incline is  60.049 degrees.

 

http://www.csgnetwor...egradecalc.html

 

http://www.1728.org/gradient.htm

 

The problem others have had with answering this question is that using a protractor on the image I uploaded doesn't work. The image is not a cross-section of the hill it's a graph, and if you resize it you will constantly get different 'protractor' measurements.

 

And, YES, if you saw the hill or had to walk up that hill you would know it's far more steeper than 7-8 degrees suggested.


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#13
SpywareDr

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Okay, so let's draw it. The graph in your original message above supplies both the length and the height of your climb.

Length - The lowest point at the beginning of your climb is roughly at the 117 meter mark and the highest point at 7 meters. 117 meters minus 7 equals a total of 100 meters between the lowest and highest points.

Height - The lowest point at the beginning of your climb begins at a height of roughly 193 meters and the topmost point of 211 meters. 211 minus 193 equals a total height of 18 meters.

So, we have 100 meters long by 18 meters tall. Let's get it on paper:
 

  • Lay a sheet of graph paper in front of you horizontally (landscape), and beginning at the bottom left corner, start counting the squares one by one off to the right until you reach 100 squares, and put a dot there at the bottom edge of the paper.
     
  • Back at the bottom left corner of the graph paper, start counting the squares up the left edge one by one until you get to 18 squares, and put a dot there at the left edge of the paper.
     
  • Take a ruler and draw a straight red line from that left dot you just made down to the rightmost dot. That is the angle of the hill.

    hill_on_graph_paper.jpg
     
  • Now take a protractor and place it's center on the rightmost dot you made, making sure that the bottom edge of the protractor is aligned with the bottom edge of the paper. Now look at the degree markings along the left arc of the protractor and what is the angle of the red line?

    hill_with_protractor.jpg

    I see close to 15-1/4 degrees.

 


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