I'm really lost on this problem

Since you need a little bit of trigonometry to solve this problem,
I'm pretty sure you've had a little bit of trigonometry in class before
you were assigned to solve this problem.

-- The shaded triangle comes from taking the equilateral triangle and
either folding it in half or cutting it in half.

-- The base that the new triangle is standing on is 1/2 the base of the
equilateral triangle, so it's 7 cm long.

-- The acute angle at the right end of the base is the same as it was in
the equilateral triangle . . . 60 degrees.

--  The tangent of 60 degrees is (opposite side)/(adjacent side) = x / 7 cm

              tan(60) = x/7

-- Multiply each side of this little equation by 7 :   7 tan(60) = x
 
If you don't have the tangent of 60 degrees in your pocket, you can
find it with your calculator.  Multiply it by 7, and Shazam, you know 'x' .