I want to see the calculations.

That's quite a long name you have.

R = (Vo^2/g)*sin(2A) = 20,000 m

sin(2A) = 0.785

2A = 51.7 or 128.3 degrees
A = 25.85 or 64.15 degrees

the range of a target is found to be 20 km. a shell leaves a gun with a velocity of 500m/s. what must be the angle of elevation of the gun if the ground is level?

Certainly! If you have a specific question or calculation in mind, please provide the details and I'll be happy to walk you through the process step-by-step.