One side of a right triangle is known to be 15 cm long and the opposite angle is measured as $30^\circ$, with a possible error of $\pm 1^\circ$.
(a) Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.)
(b) What is the percentage error? (Round your answer to the nearest integer.)
I've tried this several times now but I keep getting it wrong. So I start with $h=\frac{15}{\sin(\theta)}$ and then I used the quotient rule to take the derivative of both sides and multiplied by $d(\theta)$ and I got $dh=\frac{-15\cos(\theta)}{\sin^2(\theta)}*d(\theta)$ but when I plugged in $30$ and $1$. I got the wrong answer. Can somebody tell me how to do this problem? I very frustrated with it.