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have you ever stood on a Sandy Beach
gazing out at the vast sea or at the
edge of a high hill and wondered where
does the Horizon end how far can my eyes
see those disappearing boats it's one of
those questions that Sparks curiosity in
everyone but before we get into math
let's understand what the Horizon is the
Horizon is the line where the Earth's
surface seems to meet the sky but here's
the catch the Earth isn't flat it's a
giant sphere sorry flat earthers so what
you're seeing is actually the curved
edge of the Earth and that's why the
Horizon appears where it does the
distance to this line depends on how
high you are above the ground the higher
you go the farther you can see imagine
the Earth as a giant ball if you were
standing on the surface of this ball
your eyes would form a straight line
line pointing outward this line
eventually meets the curved surface of
the ball creating what we call the
Horizon to calculate how far this point
is from where you're standing we'll need
to think about this triangle whose one
side is the straight line from your eyes
to the Horizon another side is this one
which is equal to Earth's radius plus
this height now this can be anything on
the surface of the Earth if you are
standing on a Sandy Beach be gazing out
at the vast sea then this height will be
your actual height and if you are at the
edge of a high hill then this height
will be the same as the height of the
Hill plus your actual height and the
third side is this one which is simply
the Earth's radius because the Horizon
is on the Earth's surface since this is
the tangent line and this is the radius
therefore this angle will be the right
angle now to solve this problem we need
two important measurements
the radius of the Earth and your height
above the ground as explained before
scientists have already measured the
Earth's radius to be about
6,378
km now if you're standing at sea level
your height might be around 6 ft or
nearly 1.8 m thus we can simply use the
Pythagoras Theorem to solve for this
length label this as H for Horizon let
us label the radius of the Earth as R
and our height as l so we get h² + r² =
R + L whole Square expanding this gives
us r² + 2 R L + L S R square gets
canceled out and after taking L as
common here we are left with L * 2 R + L
that is simply amazing so we have H
equal the square < TK of L * 2 R + L let
us substitute the values of R and L to
get H as nearly 4.8 km so if you're
standing at sea level The Horizon is
about 4.8 km away this is mind-blowing
isn't it now what happens if you go
higher assume if you're on a hill or a
tall building this L will be greater
let's say you're stand standing on a
hill that is 100 m High including your
height now when we substitute the values
of R and L we get H as nearly 35.7 km
which is about the distance between two
small towns or across a large part of a
city that's a big difference if you
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