Analyze the diagram find the value of y

Answer B:  y = 4√3/3, or y = 4/√3

Step-by-step explanation:

Here we have two 30-60-90 triangles, and because of this we know the triangles are similar.  Given that the longer hypotenuse is 8 and the angle adjacent to it is 30 degrees, we state that the shorter leg of the larger triangle is determined by

sin 30 degrees = opp / hyp, or sin 30 degrees = opp / 8.  Then the shorter leg of the larger triangle (that is, the vertical leg) is 8 sin 30 degrees, or 4.

Now 4 is the length of the longer (vertical) leg of the smaller triangle.  In the same way as we found 4 (above), we write:

tan 30 degrees = y / 4, or   y = 4 tan 30 degrees, or y = 2.31.  This is equivalent to Answer B:  y = 4√3/3, or y = 4/√3.