Using differentials to estimate error

[Buka]

one side of a right triangle is known to be 12 cm long and the opposite angle is measured as 30°, with a possible error of ±1°.
(a) Use differentials to estimate the error in computing the length of the hypotenuse.

 

[MarkFL]

Hello and welcome to MHB! :D

I have retitled your thread so that the title now reflects the nature of the question being asked.

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

 

[HallsofIvy]

one side of a right triangle is known to be 12 cm long and the opposite angle is measured as 30°, with a possible error of ±1°.
(a) Use differentials to estimate the error in computing the length of the hypotenuse.

[math]sin(\theta)= \frac{a}{c}[/math] so that [math]c= \frac{a}{sin(\theta)}= \frac{12}{sin(\theta)}= 12(sin(\theta))^{-1}[/math]. Differentiating, [math]dc= -12(sin(\theta))^{-2} cos(\theta) d\theta[/math].

Take [math]\theta= 30^o[/math] and [math]d\theta= \pm\frac{\pi}{180}(1)= \pm\frac{\pi}{180}[/math] (because the derivative of sine assumes the angle is in radians, not degrees).