Hi there,

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' $\displaystyle a = b \frac{\sin A}{sin B}$ holds.

Now, suppose we have approximate values $\displaystyle b = 4m \pm 0.04m, A = \pi/2 \pm 0.01 and B = \pi/3 \pm 0.01$ (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.