Hello, symmetry!

You need a better diagram . . .

The tallest building in the world is the Sears Tower in the city of Chicago.

If the observation tower is 1450 feet above the ground,

how far can a person see standing in the observation tower

using the fact that Earth's radius is 3960 miles? Code:

*
| \
h| \
| \d
* * * \
* | *
* | /*
* R| / *
| / R
* | / *
* * *
* *
* *
* *
* *
* * *

The height of the tower is $\displaystyle h.$

The radius of the earth is $\displaystyle R.$

The distance from the top of the tower to the horizon is $\displaystyle d.$

$\displaystyle d$ and $\displaystyle R$ form a right angle.

From the right triangle: .$\displaystyle d^2 + R^2\:=\:(h + R)^2$

. . which simplifies to: .$\displaystyle d^2\:=\:2Rh + h^2\:=\:h(2R + h)$ **[1]**

We are told that: .$\displaystyle R = 3960$ and $\displaystyle h = \frac{1450}{5280} = \frac{145}{528}$

Substitute into **[1]**: .$\displaystyle d^2\:=\:\frac{145}{5287}\left(2\cdot3960 + \frac{145}{528}\right) \:=\:2175.075417$

Therefore: .$\displaystyle d \:\approx\:46.63$ miles.