I've got a question which I'm not entirely sure how to approach. The question is:
Suppose that a triangle has side lengths, a, b and c and angles A, B and C with the angle A opposite a, B opposite b and C opposite c. Then you are given that the 'sine rule' holds.
Now, suppose we have approximate values (A and B in radians). What is the approximate maximum error in a given by the formula above (obtained from a linear approximation)?
I'm confused by the linear approximation statement. Do I have to find a linear approximation for the sine rule, then calculate the errors by that approximation? Do I differentiate the sin rule and figure the error out that way?
Thank you for your time.