If cos(x)=1/2, what is sin(x) and tan(x)? explain your steps in complete sentences

The cosine of an acute angle in a right triangle  is the ratio of the length of the adjacent side to the length of the hypotenuse.

If cos(x)=1/2, then: 
the adjacent side = 1
the hypotenuse = 2

By the Pythagorean theorem:
the opposite side = √(2² - 1²) = √(4-1) = √3

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse, so:
sin(x) = opposite/hypotenuse = √3/2

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: 

tan(x) = opposite/adjacent =√3/1 = √3