Question

Analyze the diagram below and complete the instructions that follow.

Answer 1

The large triangle is isosceles, so that the two smaller triangles that appear inside the large one have bases of 12/2, or 6.

Let's see how x and y are related:

sin 60 degrees = opp/hyp = x/y = sqrt(3) / 2

and  cos 60 degrees = adj/hyp = 1/2 = 6 / y.  Then y = 12 (which should be no surprise, since the large triangle is equilateral).  

Then:  x/y = sqrt(3) / 2, or

 x        sqrt(3)       x
---- = ----------- = ------ , so that 2x = 12sqrt(3), or x=6sqrt(3).
  y           2           12

In summary, 
x = 6√3
y=12