In △ABC, m∠A=104∘, m∠B=36∘, and m∠C=40∘. Order the sides from shortest to longest. Triangle ABC A. AB¯¯¯¯¯¯¯¯,BC¯¯¯¯¯¯¯¯,AC¯¯¯¯¯¯¯¯ B. AB¯¯¯¯¯¯¯¯,BC¯¯¯¯¯¯¯¯,AB¯¯¯¯¯¯¯¯ C. AB¯¯¯¯¯¯¯¯,AC¯¯¯¯¯¯¯¯,BC¯¯¯¯¯¯¯¯ D. AC¯¯¯¯¯¯¯¯,AB¯¯¯¯¯¯¯¯,BC¯¯¯¯¯¯¯¯ i need the answer fast!

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4