# Estimate the maximum allowable percent error

• Apr 5th 2013, 01:22 PM
dangbeau
Estimate the maximum allowable percent error
The measurement of one side of a right triangle is found to be 9.5 inches, and the angle opposite that side is 26°45' with a possible error of 15'. Estimate the maximum allowable percent error in measuring the angle if the error in computing the length of the hypotenuse cannot exceed 2%.
What should I do first? Pls show me the way to solve it
• Apr 5th 2013, 05:59 PM
hollywood
Re: Estimate the maximum allowable percent error
You first need to write an equation for the length h of the hypotenuse in terms of the side you have and the angle $\displaystyle \theta$. That's pretty elementary trigonometry. Then differentiate h with respect to $\displaystyle \theta$ and divide by the original equation. That should give you $\displaystyle \frac{dh}{h}$ in terms of $\displaystyle \frac{d\theta}{\theta}$. Then you set $\displaystyle \frac{dh}{h}=0.02$ and solve for $\displaystyle \frac{d\theta}{\theta}$.

But it seems like you already have the percent error for the angle: (15' / 26°45') x 100%. So are you trying to find out if that's too much?

- Hollywood