How to calculate error in taylor series step by step?

[safranta]

The height of a tower is measured at the angle of two different points in the same direction on the ground. The angle of the M point to the tower is [tex]\beta[/tex] = 50° and the angle of the N point to the tower is [tex]\alpha[/tex] = 35, these angles are most often measured with a variation. MN interval was measured with a maximum error of 0.1% x = 100m.

1-What is the calculated height of the building, what is the error at the calculated height?
2-For which measurement (x, [tex]\beta[/tex], [tex]\alpha[/tex]) the calculated height is more
sensitive,
3-why?

[Guest]

If we call the height "h" and the distance from M is "d" then h/d= tan(50).
The distance to N is d+ 100 so h/(d+ 100)= tan(35). From the first equation h= d tan(50) so d tan(50)/(d+ 100)= tan 35. d tan(50)= d tan(35)+ 100 tan 35. d(tan(50)- tan(35))= 100 tan(35) so d= 100 tan(35)/(tan(50)- tan(35)) and then h= d tan(50).

You say that "MN interval was measured with a maximum error of 0.1%". 0.1% of 100 is 0.1 so MN might be as large as 100.1 or a small as 99.9. you can calculate d with d= 100.1 tan(35)/(tan(50)- tan(35)) again with d= 99..9 tan(35)/(tan(50)- tan(35)), then h= d tan(30), and subtract to find the error.

You say "these angles are most often measured with a variation." but don't say what that variation is so no precise answer can be given.