Help me I'm lost in the ocean!
05AB1E, 13 12 10 bytes

Saved 2 bytes thanks to Emigna.

Since there is no trigonometric functions to be called using OP's assumption that the earth is locally a plane, it becomes possible to make an 05AB1E solution.

•1#oC•+¹*t

           For understanding purposes input is referred to as 'h'
•1#oC•     Push 12742000 [ = 2*R, where R is the radius of earth]
      +    Compute 2*R+h
       ¹*  Multiply by h. Result is (2*R*+h)*h
         t Take the square root of it and implicitly display it


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