Plz explain this example

[umer007]

tan(θ°) = (viv) / (vih)

= (1.28 ± 0.0676m/s) / (0.514 ± 0.0676m/s)

= 2.55 ± 0.467 m/s

θ° = 68.0 ± 3.65°

 

This answer may not be correct to the decimal place but it shud b relatively close. Could someone plz explain to me how 3.65° becomes the uncertainty for the angle? Plz. explain very clearly and simply. Im in a hurry.

 

THanks in advance

[timo]

There are many possibilities of doing error-calculations. The (mathematically) easiest would be errorangle = max{ arctan(2.55+0.467)-arctan(2.55), arctan(2.55)-arctan(2.55-0.467) }. The same can be applied for getting the 0.467. Just take the max and min that the fraction can become and take the maximum deviation from 1.28/0.514.

For the error it´s usually more important to have it in the correct order of magnitude than having an exact result. If it´s your measurement then you should know youself how to get a sensible error-approximation. If it´s someone else´s there´s usually not much to bother about how someone derived his/her error approximation (unless the number is extraordinarily large or small).