Anybody know how to do this?

Evaluate cos2θ for cosθ = square root of 3/2

Mr. brettler is hanging up a 5-foot tall rectangular welcome sign in the gym. he has drawn a sketch on a coordinate grid. he has the lower vertices of the sign at (9, –3) and (–6, –3). where would the upper vertices be on the grid?

Find the value of x. give reasons to justify your solutions! l, m ∈ kn