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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.

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

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 $\Delta y$

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  • $\begingroup$ 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

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