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Maatsuyker Island lighthouse is the last Australian lighthouse still being officially operated by lightkeepers. The lighthouse is 15m high from its base to the balcony, and located 140m above sea level. The caretaker is standing at the balcony and notices a ship at the horizon. Find the straight line distance from the lighthouse balcony to the ship

 Jul 16, 2019

We need to know the radius of the Earth (in meters)   ≈ 6,370,000 m


We have a right triangle with a hypotenuse of the radius of the Earth + height of lighthouse above sea level =  [6,370,000 + 140 + 15 ] m = 6,370,155 m


The distance from the center of the Earth to the ship  is just the Earth's radius and forms one leg of the triangle


And the distance we are looking for is the other leg of the triangle  = D


So....by the Pythagorean Theorem :


D  = √ [ 6,370,155^2 - 6,370,000^2 ]  ≈  44,438 m  =  44.438 km  ≈ 27.5 miles



cool cool cool

 Jul 16, 2019

Thank you very much! smiley

Guest Jul 16, 2019

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