The problem states that the cosine of angle [tex]\( x \)[/tex] in the original triangle is given by [tex]\( \frac{8}{17} \)[/tex].
When a triangle is dilated, the angles within the triangle remain unchanged. Dilation involves scaling all sides of the triangle by the same factor, which does not affect the internal angles of the triangle. Therefore, the trigonometric ratios, which are dependent only on the angles, also remain unchanged.
Hence, the value of [tex]\( \cos(x) \)[/tex] for the dilated triangle is the same as the value of [tex]\( \cos(x) \)[/tex] for the original triangle.
Thus, the value of [tex]\( \cos(x) \)[/tex] for the dilated triangle is:
[tex]\[ \frac{8}{17} \][/tex]
