Hi Edermardil ....this is the best diagram I could find that represents the situation , it's not very good but it will have to do, in our situation the angle theta will be very small ....

TP is the horizontal line projected from the battleship ...

We are told the max range of the shell is 41Km, this is the distance TP

distance OT is the radius of the Earth

distance OP is the radius of Earth plus the distance you are asked to find in question (c)...

so we have a right angle triangle ,simple geometry to find OP since we know the other two sides ...a search will get Earth's radius.