Using differentials to calculate the percentage error in the hypotenuse of a right angle triangle?

1. Use differentials to estimate the error in computing the hypotenuse



2. Calculate the percentage error



-One side of a right angle triangle = 20 cm

-opposite angle = 30 degrees

-possible error in angle =+/- 1 degree



If someone could explain this I would greatly appreciate it!



Thanks :)Using differentials to calculate the percentage error in the hypotenuse of a right angle triangle?
sin(x + dx) = O/H

x + dx = arcsin(O/H)

dx = arcsin(O/H) - x



H = O/sin(x)

H = 40



H = O/sin(x + dx)

H = 20/sin(31°)

H = 38.83



H = O/sin(x - dx)

H = 20/sin(29°)

H = 41.25



%error = (38.83 - 40)/40 * 100

%error = -2.925%



%error = (41.25 - 40)/40 * 100

%error = 3.125%