You first need to write an equation for the length h of the hypotenuse in terms of the side you have and the angle . That's pretty elementary trigonometry. Then differentiate h with respect to and divide by the original equation. That should give you in terms of . Then you set and solve for .
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?