*brainliest for best answer you* solve for b.

Hello from MrBillDoesMath!

The fourth choice,  b = +\- sqrt( sg + a^2)

Discussion:

s = (b^2 - a^2)/g     =>              multiply both sides by "g"

sg = b^2 - a^2        =>               add a^2 to both sides

sg + a^2 = b^2       =>                take the square root of each side

b = +\- sqrt( sg + a^2)

which is the fourth choice.

Thank you,

MrB