Answer: Choice C
Explanation:
This is a 45-45-90 right triangle, aka isosceles right triangle.
The two legs are 6 units each, because the legs of isosceles triangles are the same length.
The hypotenuse is 6*sqrt(2) through the use of the pythagorean theorem.
From here we can say:
[tex]\cos\left(\text{angle}\right) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos\left(45^{\circ}\right) = \frac{6}{6\sqrt{2}}\\\\\cos\left(45^{\circ}\right) = \frac{1}{\sqrt{2}}\\\\[/tex]
It turns out that the '6' has nothing to do with the final answer, since the '6's cancel out. So we could change that 6 to any number we want, and the answer would still be the same.
Side note: Rationalizing the denominator will have [tex]\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}[/tex]
