Please help calculate the percentage error?

A surveyor estimates the area of a triangular plot of land using the formula

A =1/2 absinC where a and b are the length of two sides and C is the included

angle. If the sides are measured to an accuracy of 1% and the angle C,

measured as 45掳, is measured to within 2%, calculate the approximate

percentage error in A.Please help calculate the percentage error?
Ideally, the area is 1/2 ab sin45. However, a and b have errors of 1%. Error in sin 45 when C is measured within 2% is estimated as follows. 100*(Sin45-sin43)/sin45 = 3.55%. Thus area has error of 1% due to a plus 1% due to b plus 3.55% due to C. The total worst case error is 5.55%. However one generally calculates root sum squared error and that is sqrt(1^2+1^2+3.55^2) = 3.82%. The reason for doing this is that the probability of errors being the max error is relatively small.

You may verify by taking a few values for a, b and C as a= 15, b= 10, C= 45 and compare with a= 15.15, b = 10.1 and C= 43.

Do another exercise, with C as 60 deg and another as C = 30 deg, for practice.Please help calculate the percentage error?
Push each variable to the edge of its tolerance band and then compare the result to the nominal value.