Javelin at 72 meters/second. he throws it at an angle of 22 degrees. how fast is he throwing it in the x-direction in meters/second?

Assume this is 22 degrees from the horizontal (x).
A vector can always be split into components - in this case we can think of the world in two dimensions, meaning the 72ms-1 has a vertical and a horizontal component. We therefore know the hypotenuse of the triangle (the overall velocity) and the angle from the ground. Hence we can use trigonometry to solve this problem.

We know x and the hypotenuse, and we want to know the magnitude of the adjacent side (horizontal), therefore we can use cosx=adj/hyp

Substituting:

Cos(22) = adj/72
Adj = 72cos22 = 66.8ms-1 = 67ms-1 to 2sf