Question 32560
Draw a right triangle with acute angles of 30 degrees and 60 degrees.
Let the side opposite the 30 degree angle have length "1"
Then the hypotenuse will have a length of "2".
Then, using Pythagoras, the third side will be sqrt 3

The Cosine of an angle is (adjacent)/(hypotenuse)
The side adjacent to the 60 degree angle is "1".
So the Cos 60 degrees is 1/2
Cheers,
Stan H.