The lengths of sides b and c of a triangle ABC are measured accurately, while angle A is measured with an error of 1/2 degree.
If b = 12cm, c = 15cm and angle A is 30 degrees, what is the approximate value of the error in the area of this triangle?
Our teacher wanted us to think about this in the lesson. I used the $\frac12 b c \sin (A)$ formula but couldn't find it. Do you have any comments?
Yes your idea is right and we can use that
$$\Delta S= \frac12 b c \sin (A+\Delta A)-\frac12 b c \sin (A)$$
with
$$\sin (A+\Delta A)=\sin (A)\cos (\Delta A)+\sin (\Delta A)\cos (A)$$
As an alternative we can use that
$$\frac{dS}{dA} =\frac12 bc \cos A \implies \Delta S \approx \frac12 bc \cos A \Delta A$$
with
$$\frac{\Delta A}{\Delta A°}= \frac{\pi}{180}$$