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Using Differentials to find Error and Percent Error 
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#1
Oct2007, 04:58 PM

P: 10

1. The problem statement, all variables and given/known data
One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30(degrees), with a possible error of +/ 1 degree. a) Use differentials to estimate the error in computing the length of the hypotenuse b) what is the percentage error. 2. Relevant equations 3. The attempt at a solution Well, using the given data I found that the hypotenuse when x=30(degrees) is 40 cm. The equation I used was h(x)=20/sin(x). I know that the change in (h) is equal to error x h'(x). When finding h'(x) I got 20cos(x)/sin(x)^2. I'm not sure if this is correct. My book doesn't do a great job at explaining anything so any help will be greatly appreciated! 


#2
Oct2007, 05:37 PM

Mentor
P: 41,326

You're almost there. Expressed in terms of differentials, h' = dh/dx. So write dh in terms of dx. dx will represent the error in angle (be sure to express dx in radians, not degrees); the equation for dh will tell you the corresponding error in the hypotenuse.



#3
Oct2007, 08:12 PM

P: 10

so do I do ( 20cos(30)/sin(30)^2 ) x pi/180? if so I got 1.209. Can error be negative? Or since it's both +/ 1 degree, do you also do another equation multiplying by a negative pi/180. My real questions are, how is error represented (multiple numbers, one number, a continuum)? And, how do I go about converting this to a relative error, and then percent error.
Thanks! 


#4
Oct2107, 06:05 AM

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P: 41,326

Using Differentials to find Error and Percent Error



#5
Oct2107, 06:08 PM

P: 10

I love this forum. Thanks for all the help!



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