Imagine this triangle

We are interested in

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

$$b=\sqrt{7^2-4^2}$$ $$b=\sqrt{33}$$

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.


$$\frac{\Delta y}{y}=\frac{1}{2}.\frac{\Delta x_1}{x_2}+\frac{1}{2}.\frac{\Delta x_2}{x_2}$$

You already have calculated $y$. You have $x_1 =7$ with error of $\Delta x_1=0.1$ . Same with $x_2=4$ with error of $\Delta x_2=0.3$.(please assum units in $km$)

Simply calculate $\Delta y$

  • $\begingroup$ Little typo $x_2$ instead of $x_1$ in the third fraction $\endgroup$ – Jean Marie May 2 '17 at 14:36
  • $\begingroup$ Thanks! This helps. One further question: How do I compare $\Delta y$ with the error that would have occurred during a measurement without clouds based on the second device? $\endgroup$ – Phaneron May 2 '17 at 14:36
  • $\begingroup$ @Phaneron If you find the answer helpful. you may accept it. $\endgroup$ – The Dead Legend May 3 '17 at 3:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.