Do you know the correct approach to this kind of question?
Draw a right triangle situated in the first quadrant, for which tan θ = 15/8.
Thus the hypotenuse will be 17 (this is one of the Pythagorean triples).
Note: you are being asked to get cos θ BECAUSE θ = ARCTAN 15/8.
Do you see it?
You can even check this on your calculator.