How does radius of the earth connected to the geometric problem specially this one?

Question

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).

Specifically how radius of the earth is connected to this problem?

Additionally,what will be the solutions for ships and planes?

Answer 1

Having the radius of the earth helps us to find the distances of objects in horizon and beyond that.

Answer 2

The top of the lighthouse, the centre of the earth and a point at sea level from which the light is on the horizon form a right triangle.