How high and how large would you need a shadow shield to form a 250 mile wide shadow on the ground?

Just what it says.

How large of a shield in Earth orbit would you need to cast a 250 mile wide shadow on the surface of the Earth.

Could you put it in very low Earth orbit and maintain its position by constant thrust?

In LEO it would need to be about 251 miles in diameter, but there's no way to maintain it's position relative to the surface without building continuous rings in stacked orbits with varying angles of inclination.

Trigonometry for beginners.

Monty, is that you?