Question 1208415: A person who is 6 feet tall is standing on the beach in Florida and looks out onto the Atlantic Ocean. Suddenly, a ship appears on the horizon. How far is the ship from shore?
A friend told me to use the following facts and formula.
d = distance the ship is from shore
r = radius of Earth = 3960 miles
m = number of feet in a mile = 5280
h = height of the person standing on the beach in Florida
d^2 + r^2 = [(r + (h/m)]^2
We want d.
d^2 + (3960)^2 = [(3960) + (6/5280)]^2
Is my friend correct?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Make a sketch. The Earth is a sphere (not flat) - so, draw a circle representing the spherical Earth
of the radius r = 3960 miles.
On the top of the circle, draw a person h = 6 ft =  miles tall, standing on the Earth.
From the level of the person's head, draw a tangent line to the Earth.
This tangent line will represent how far this person sees the surface of the ocean.
Also, draw the radius of the Earth to the tangent point.
On the sketch, you will see the right-angled triangle with the hypotenuse length of
r + h = 3960 + miles
and one leg of the length r = 3960 miles.
So, you can find the other leg of this triangle, which is a tangent to the Earth surface,
from the Pythagorean equation
d^2 + r^2 = (r + h)^2.
Here "d" is the distance to the horizon, in miles.
So, your friend is right.
Calculations give d =  = 3 miles.
Solved, answered, and explained.
|
|
|
