If the cos of angle x is 8/17 and the triangle was displayed to be two times big as the original what would be the value of the cos of x for the dilated triangle

Answer: The value of cos(x) of the dilated triangle would be exactly the same as in the first triangle, cos(8/17).

The cosine ratio is a ratio of two sides. 

In the first triangle the ratio is 8/17.

In the second triangle the ratio is 16/34. This could be reduced back to 8/17 which would produce the same cosine value.