Determine the angle A in the picture below:

A
B
C
D

The answer is B

Step-by-step explanation:

This is a right triangle and a triangles angles can only add up to 108 degrees. In addition the angle is very small as it looks showing it must be one of the smallest answers aka, B.

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