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tan z  =   opp / adj  =  3 /  1

The hypotenuse =  sqrt [ 3^1 + 1^1 ] =  sqrt (10)

cos z  = adj / hyp  =    1 /sqrt (10)  =  sqrt (10) / 10

In a right triangle XYZ where angle X is 90 degrees, we can use the information provided to find the cosine of angle Z.

Given that tan Z = 3, we know that:

$$\tan Z = \frac{\text{opposite}}{\text{adjacent}} = \frac{YZ}{XZ} = 3.$$

Since triangle XYZ is a right triangle, we can use the Pythagorean theorem:

$$XY^2 + YZ^2 = XZ^2.$$

Since angle X is 90 degrees, we have:

$$XZ^2 = XY^2 + YZ^2 = YZ^2 + YZ^2 = 2YZ^2.$$

Solving for YZ:

$$YZ^2 = \frac{XZ^2}{2}.$$

Since we know the value of YZ/XZ (which is the tangent of angle Z):

$$\tan Z = \frac{YZ}{XZ} = 3.$$

Squaring both sides:

$$YZ^2 = 9XZ^2.$$

Now, substituting the value of YZ^2 from the Pythagorean theorem:

$$9XZ^2 = \frac{XZ^2}{2}.$$

Solving for XZ:

$$\frac{XZ^2}{2} = 9XY^2.$$

$$\cos Z = \boxed{\frac12}.$$