Question

(Calculus) One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 degrees, with a possible error of measurement of 1 degree. Use differentials to estimate the error in computing the length of the hypotenuse.

No idea how to approach this problem. Missed this lesson in class...

Answer 1

no takers?

Answer 2

we know that sin(theta)= 20/H where θ = pi/6
therefore H = 20/sinθ
so now we find dH/dθ

Answer 3

see how you go from here

Answer 4

ah yes I see.. Is it as simple as that?? \[dH=\frac{20\cos \theta}{\sin^2 \theta} \times d \theta\]

Answer 5

Is this correct?

Answer 6

what is d theta though? I know i have to plug in 30 degrees to the other thetas.

Answer 7

you have to be very careful with dθ.
In calculus always work in radians, so dθ is .0175 radians

Answer 8

.0175 radians is equivalent to 1 degree

Answer 9

Oooh. I see. But if I keep it in degrees, it should come out to (I corrected my equation from before)\[dH=\frac{-20\cos (30)}{\sin^2 (30)}*\frac{\pi}{180}?\]

Answer 10

well pi over 180 is basically .0175 haha. don't know if this is the right way though..

Answer 11

this will work but its always best to stick to radians

Answer 12

its correct. well done

Answer 13

so instead of 30, I should use pi over 6?

Answer 14

strictly speaking yes

Answer 15

okay awesome. It makes better sense to do radians now that I'm thinking more thoroughly about it. Thanks so much. (: This will help on my finals.

Answer 16

no problem. you should get an answer of dH = 1.212 cm

Answer 17

great problem. thanks for posting