Estimate relative error using differentials

[DevoMci]

Area of right triangle with hypotenuse H is

A=(1/4)H^2sin(2theta)

where theta is one of the acute angles.

Use differentials to estimate the relative errors of the area A if H=4cm and theta is measured to be 30 degrees with an error of measurement of 15 minutes of arc.

note: a minute of arc, 1' is approximately equal to (1/60) of a degree.

I'm not quite sure what a measurement of arc is and whether I'm supposed to find the derivative or what? I am so lost, thanks in advance.

 

[Mark44]

Area of right triangle with hypotenuse H is

A=(1/4)H^2sin(2theta)

where theta is one of the acute angles.

Use differentials to estimate the relative errors of the area A if H=4cm and theta is measured to be 30 degrees with an error of measurement of 15 minutes of arc.

note: a minute of arc, 1' is approximately equal to (1/60) of a degree.

I'm not quite sure what a measurement of arc is and whether I'm supposed to find the derivative or what? I am so lost, thanks in advance.

You need to find the differential of A, dA. Your book should have some examples of how to find the differential.

Also, unless I'm missing something, one minute of arc, 1', is exactly equal to 1/60 of a degree.