Find approximate error

Question

at a distance of 50 meter from foot of tower the elevation of its top is 30 degree if the possible error in measuring the distance and elevation are 2cm and 0.05 degrees find approximate error in calculating the height

Answer 1

tan 30 = H/50 ---> 50 * tan 30 = h

50*Sqrt(3)/3 = h

However, the distance is in [49.98, 50.02] and the angle is (29.95,30.05), given these error margins.

The height with the EXACT measures is 28.867513459481288225457439025098

The height with the MINUMUM values in these ranges is 28.79784.

The height with the MAXIMUM values in these ranges is 28.93729

So the error for the MIN values is |28.79784 - 28.86751|/ 28.86751 = 0.241344%

and the error for the MAX values is |28.93729 - 28.86751|/28.86751 = 0.241725%