We have that tan x = 6/11.

tan x is equal to the opposite side/ adjacent side for the angle in a right triangle.

Using the Pythagorean theorem we calculate the length of the hypotenuse as sqrt ( 6^2 + 11^2) = sqrt ( 36 + 121) = sqrt 157.

Now, cos x = adjacent side/ hypotenuse

=> 11 / sqrt 157.

**cos x = 11 / sqrt 157**