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Error Propaganda and Differentials?
The question reads as follows:
One side of a right triangle is known to be 25 cm exactly. The angle opposite to this side is measured to be 60 degrees, with a possible error of +/-0.5 degrees.
(a) Use differentials to estimate the errors in the adjacent side and the hypotenuse.
(b) Estimate the percentage errors in the adjacent side and hypotenuse.
So far all I've been able to do is figure out the length of the hypotenuse and adjacent side (i'm not even sure if I needed to...) but those numbers are approx. 28.9 degrees for the hypotenuse and approx. 14.4 degrees for the adjacent side.
I'm not just asking for the answer, just wondering the steps I need to use so that I can find the answer on my own. Thanks.
1 Answer
- Sue_CLv 51 decade agoFavorite Answer
Let X be the length of the adjacent side, H the length of the hypotenusa. Let A be the given angle and x,h and a all the errors.
If I understood the question correctly, then we have
H=25/sin A and X=25/tan A.
And for the errors we propagate the error of A:
h^2 =a^2 (dH/dA)^2 and x^2=a^2 (dX/dA)^2
