Imagine this triangle
and the distance between city A and C.
Unfortunately, the clouds block the measurements of our telemetric devices. However, we once measured the distance between city A and B as $7$ km and the device we applied at that time had a measurement error of $0.1$ km.
We now measure the distance between city B and C with a second device bearing measurement error of $0.3$ km. We find that distance to be $4$ km.
Calculating the distance between A and C
Using the pythagorean theorem I calculate
What is the maximum error occuring with my approach?
I know I'm supposed to use differentials to calculate the maxiumum error here. But I'm unable to come up with an equation at the moment. Help is very much appreciated.