One side of a right triangle is known to be 13 cm long and the opposite angle is measured as 30°.?
with a possible error of plus or minus 1 degree.
(a) Use differentials to estimate the error in computing the length of the hypotenuse.
(b) What is the percentage error?
I thought to use the pythagorean theorem but the answer I come out with is wrong.
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is the 1st answer 0.785? anyway the method is to write the relation: length=13/sinx where x=30 deg. Now differentiate it partially wrt x so dlength will give u the error in hypo length.
and then % error is the simple matter of dividing the whole differential by ur original relation so as to get dx/x. cheers
(a)
13/h = sin(x)
h = 13/sin(x) = 26 at x = 30 deg.
dh = 13cos(x)/sin^2(x) dx
dh â [13cos(30)/sin^2(30)] (2/180) = 1.955
(b)
dh/h = 7.52%
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Ideas: You have to use radians for dx.