A particular type of bridge can fold up to allow boats to pass by. Each folding part of the bridge is 64 m long and makes a 70° angle to the horizontal when fully raised. How far apart are the ends of the raised parts when the bridge is fully
opened?

what is all that apply?

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