SOLUTION: 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

Question 1207473: 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?
Answer by ikleyn(52832) (Show Source): You can put this solution on YOUR website!
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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) A brochure states that the light itself can be seen on the horizon about 26 miles distant.
Verify the correctness of this information.
(b) 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?
~~~~~~~~~~~~~~~~~~~~~~

I will solve and answer part (a), ONLY.

Make a sketch. In the sketch, you will see a circle representing the Earth,
with the radius of 3,958.8 miles.

Also, you will see a right-angled triangle with the hypotenuse length of

      R + h = 3958.8 +  = 3958.8 + 0.06856 = 3958.87 miles

and one leg of the length R = 3958.8 miles.


So, you can find the other leg of this triangle, which tangents the Earth surface

    L =  =  = 23.5 miles (rounded).


It is the distance to the horizon from the top of the lighthouse.

Solved.

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