How does radius of the earth connected to the geometric problem specially this one? In Sullivan's textbook I got this problem,but I cannot make the solution to this(Using Pythagorean theorem): > The Gibb’s Hill Lighthouse, Southampton, Bermuda, in operation since $1846,$ stands $117$ feet high on a hill $245$ feet high, so its beam of Light is $362$ feet above sea level. A brochure states that the light Itself can be seen on the horizon about $26$ miles distant. Verify the Correctness of this information.The brochure further states that ships $40$ miles away can see the light and planes flying at $10,000$ feet can See it $120$ miles away. Verify the accuracy of these statements.What Assumption did the brochure make about the height of the ship? (Use $3960$ as the radius of the earth). ![enter image description here]( Specifically how radius of the earth is connected to this problem? Additionally,what will be the solutions for ships and planes?

Having the radius of the earth helps us to find the distances of objects in horizon and beyond that. ![enter image description here](