Final answer:
The cosine of angle x cannot exceed 1; thus, cos x = 5/3 suggests a typographical error. To find the tangent of an angle where the cosine is given and valid (<=1), one would use the Pythagorean identity to find sine and then divide sine by cosine.
Step-by-step explanation:
The question concerns a right triangle with an acute angle x. Given that cos x = 5/3 is impossible as the cosine of an angle cannot be greater than 1, there appears to be a typo or mistake in the question. For any acute angle in a right triangle, the cosine value, which is the ratio of the adjacent side to the hypotenuse, must be between -1 and 1.
However, if cos x were a valid number less than or equal to 1, we could find tan x (the tangent of angle x), which is the ratio of the opposite side to the adjacent side of a right triangle, using the trigonometric identity tan x = sin x / cos x. To do this, we need to find sin x using the Pythagorean theorem (sin x = sqrt(1 - cos^2 x)) and then divide sin x by cos x to find tan x.