Stefan has been given two segments and the measure of an angle between them. he is trying to construct a congruent triangle. he has just finished one of the steps of the construction. which step has he just finished?

Copy the second line segment with one endpoint at the same endpoint of the first line segment.

the square root of what number? if you add that, then someone will probably answer the question.

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