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).

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

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

• The earth is round. Feb 3, 2017 at 13:59
• I make it 23.3 miles, not 26, because $\sqrt{(3960\frac{362}{5280})^2-3960^2} \approx 23.3$. Feb 3, 2017 at 14:30
• @TonyK I know that but what will be the solution for ship and planes Feb 3, 2017 at 14:39
• On a flat earth, you can't go past the horizon, you are always visible.
– user65203
Feb 3, 2017 at 15:03
• You knew that already? Good. Then you can work out the rest for yourself, can't you? Feb 3, 2017 at 18:04