The terminal point determined is in what quadrant?

  quadrant 4

Step-by-step explanation:

I find it helpful to remember that the cosine is positive in the right half-plane, and the sine is positive in the top half-plane. Knowing the relationship between sine and cosine and all the other trig functions, you can figure their signs in the various quadrants.

The bottom half-plane (sin < 0) and the right half-plane (cos > 0) overlap in the 4th quadrant.

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