How Do You Calculate Change in Elevation on a Railroad Incline?

[Medgirl314]

Homework Statement

A 6.0 mile long section of railroad has an angle of inclination of 2.1 degrees. Find the change in elevation over the 6 miles. Give your answer in feet.

Homework Equations

sine=opp/hyp

The Attempt at a Solution

Sin 2.1=6/hyp
h=6 mi/2.1sin
h=163.7 mi=864336 ft.

Seems off, but I'm not sure. I think I did something backwards, maybe?

Let's try this:
h=2.1sin/6 mi
h=0.006 miles.

h=32.25 ft.

This seems further off.

 

[scurty]

The elevation gain would be the "opposite" side of the angle, not the hypotenuse.

 

[Chestermiller]

The opposite side should be the hypotenuse times the sine of the angle, not divided by the sine of the angle.

 

[Medgirl314]

Okay, thanks! I was trying to calculate the wrong angle.
sine=opp/hyp
sine(2.1)=opp/320 m.
0.37=opp/320
Opp=11.7 m
Opp=61776 ft.

Like that? (-:

 

[scurty]

Okay, thanks! I was trying to calculate the wrong angle.
sine=opp/hyp
sine(2.1)=opp/320 m.
0.37=opp/320
Opp=11.7 m
Opp=61776 ft.

Like that? (-:

That is how you would solve for a height, given a hypotenuse of 320m and angle of 2.1 degrees, yes.

A few remarks. sin(2.1) should be a very small number, where did 0.37 come from? The conversion from meters to feet is WAY off, double check your work!

 

[Medgirl314]

Oh, I just misread the decimal place, and then for whatever reason my brain said "HEY! Let's multiply this number by 5280!"

0.037=opp/320
Opp=11.7 m

Opp=38.5 ft.

 

[scurty]

Much better! :)

A good tip is to assess your answers after every problem; to see if they make sense. It helps in testing situations!

 

[Medgirl314]

Haha definitely. I usually do, but I'm multi-tasking. Which I will not be doing during my test. xD

 

[Chestermiller]

Haha definitely. I usually do, but I'm multi-tasking. Which I will not be doing during my test. xD

6 miles (hypotenuse) is about 30000 ft, and the sine of 2 degrees is about 0.03. So, 0.03 x 30000 is on the order of about 1000 ft.

I have a comment about your multitasking and inattention to what you are doing. Those of us who are trying to help you are contributing our valuable time. It doesn't seem fair to us for you to inattentively multitask and require 5x as much assistance because of it.

Chet

 

[Medgirl314]

Sorry, I don't get the first bit. I was intending to convert at the end, are you just trying to show that we could have done it in the beginning? I think the angle I need to use sine for is 2.1 degrees. Did you think the answer was wrong, or are you just showing a different way to do it?

I think we have different understandings of "multitasking." I was just thinking about several other things, I wasn't goofing off while posting the answer. It was a lighthearted joke. I'm not being "inattentive." I missed one part of the problem, and corrected it. It's kind of you and everyone else to try to help, but I don't require your assistance. I'm sure you have better things to do, so if you would rather do them, go for it! (-: Sorry for the misunderstanding!

Thanks again for your help!

 

[Chestermiller]

Sorry, I don't get the first bit. I was intending to convert at the end, are you just trying to show that we could have done it in the beginning? I think the angle I need to use sine for is 2.1 degrees. Did you think the answer was wrong, or are you just showing a different way to do it?

I'm saying that the correct answer is about 1000 ft.

 

[Medgirl314]

Thanks!

There seems to be a confusion here. Could someone please confirm either answer?

 

[scurty]

Thanks!

There seems to be a confusion here. Could someone please confirm either answer?

Sin 2.1=6/hyp
h=6 mi/2.1sin
h=163.7 mi=864336 ft.

Okay, thanks! I was trying to calculate the wrong angle.
sine=opp/hyp
sine(2.1)=opp/320 m.
0.37=opp/320
Opp=11.7 m
Opp=61776 ft.

Like that? (-:

I'm saying that the correct answer is about 1000 ft.

Sorry for the late reply, I was busy. The confusion is that I said your answer was correct for the third quote above, given that information (320m as the hypotenuse). Chestermiller is referring to your original post (2nd quote) which had 6 miles as the hypotenuse. The answers in the quotes aren't correct, but we've discussed that already.

 

[Medgirl314]

Oh, thank you! So how do I tell which is the hypotenuse if I can't see a right angle?

 

[Medgirl314]

Should I cut the triangle in half?

 

[scurty]

Oh, thank you! So how do I tell which is the hypotenuse if I can't see a right angle?

The best answer to this is to draw a triangle yourself, if you haven't been doing it yet. It really helps to VIEW the problem instead of just trying to apply a formula.

For these types of problems, when you draw the triangle you are viewing the problem from the side. Think of it as someone driving on a road and all of a sudden they start going uphill at a 2.1 degree angle. From this you can construct the triangle. A picture would help better explain it. The right angle is the corner of the triangle below:

 

[Medgirl314]

Okay, I see it now. Thank you! I usually try to draw diagrams, but I already had one. The angle of inclination was just so small that there seemed to be two right angles, even though that's not possible.