1. The problem statement, all variables and given/known data The area of a triangle is (1/2)absin(c) where a and b are the lengths of the two sides of the triangle and c is the angle between. In surveying some land, a, b, and c are measured to be 150ft, 200ft, and 60 degrees. By how much could your area calculation be in error if your values for a and b are off by half a foot each and your measurement of c off by 2 degrees? See figure below 2. Relevant equations dA(x,y,z) = dA/dx dx + dA/dy dy + dA/dz dz A = 1/2*absin(c) a = 150+-0.5 ft, b = 200+-0.5 ft, c = 60+-2 degrees 3. The attempt at a solution I first used the chain rule on the Area to get dA dA = 0.5bsin(c)*da + 0.5asin(c)*db + 0.5abcos(c)*dc Setting da = 0.5, db = 0.5, and dc = 2 and plugging in my values I get a completely wrong answer (the actual answer is 338 ft^2). Something felt off about the dc, because it varied so differently than the da and db changes. I then read that the change has to be relative to the value or something like that so instead of using dc = 2 degrees, I did dc = sin(2) = 0.0349, which in fact does give me the correct answer. My question: when determining that you can substitute the change in measured values for the dx variable, how do you know how to properly relate that change with the equation? Is it calculated by the expressed change in the function? For example, when you change the measured side by 1 ft, you are calculating 1 ft into the function, but when you change by 1 degree you are calculating sin(x+1) in the function. I'm trying to understand this better, thanks!