# Thread: Estimate the maximum allowable percent error

1. ## 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

2. ## 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 $\theta$. That's pretty elementary trigonometry. Then differentiate h with respect to $\theta$ and divide by the original equation. That should give you $\frac{dh}{h}$ in terms of $\frac{d\theta}{\theta}$. Then you set $\frac{dh}{h}=0.02$ and solve for $\frac{d\theta}{\theta}$.

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

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### how to estimate the maximum permissible percentage error

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