Find the exact value by using a half-angle identity. cos(5π/12).

First of all in order to find the exact value by using a half angle identity we will do
cos(5π divided by 12)

=cos (5π divided by 6) divided by 2
= ± Under root[(1+cos (5π divided by 6) divided by 2]
Now we will consider + sign because 5π divided by 12 is in quadrant. where cos>0
so the solution is [(1- Under root 3 divided by 2) divided by 2] 
We will ignore the negative sign
I hope it helped.

Yes i could be the length of the triangle