Differentiate Trig Homework: Find Uncertainty in Measured Angle

[lovemake1]

Homework Statement

we have been doing some error analysis in school, but they were very straight forward for example. Centripetal Acceleration : Fc = 4pi^2 m R / T^2


however, for my project i must find the uncertainty in the angle that i measured.
the angle is formed by a cardboard sitting on pile of books creating a triangle.
Hypothenus = 33cm
Height = Variable ( Changes according to the stack of the book)

please help ! differentiate theta = inverseSin(Opposite/Hypothenus)

Homework Equations

theta = inverseSin(Opposite/Hypothenus)

The Attempt at a Solution

well since i measurd these distances with a ruler

the uncertainty for hypothenus would be +- 0.005m (last half digit of a number)
and the uncertainty for heght is the same + - 0.005m (last half dight of a number)

how do i use these to differentiate for one another?
which formurla would i use pleaes help !

 

[rl.bhat]

If x = a/b, then the maximum error in measurement is
Δx/x = Δa/a + Δb/b

 

[lovemake1]

d(theta)=1/sqrt(1-(o/h)^2)

now how should i ?

HELP please just differentiate for opposite and hypothenus for me please...

 

[rl.bhat]

d(theta)=1/sqrt(1-(o/h)^2)
From where did you get this expression?
What it represents?