This is a right triangle, so the the top angle is
[tex] 180-90-35 = 55 [/tex]
Now we can use the theorem that states that, in every triangle, the ratio between a side and the side of the opposite angle is constant:
[tex] \dfrac{x}{\sin(35)} = \dfrac{12}{\sin(55)} [/tex]
Solving for x, we have
[tex] x = \dfrac{12\sin(35)}{\sin(55)}\approx 8.4 [/tex]
