If you go to the ~~Sears~~ Willis Tower, can you see Michigan? We can use geometry to answer the question.

We can use the Pythagorean Theorem to find the length of the side of a right triangle: . In this case the right triangle has sides of *d *and *r* and a hypotenuse of . Therefore, the Pythagorean formula is , where *r* is the radius of the Earth, *s* is the height of the Sears Tower, and *d* is the distance one is able to see.

Using FOIL to expand gives:

Since is on both sides, we can eliminate it.

.

The radius of the Earth is *r*=3,963 miles and the height of the Sears Tower in miles is *s*=0.275379 miles. Consequently, *d*=46.72 miles. The distance across Lake Michigan is just over 50 miles, so NO, we cannot see all the way to Michigan.

*Note: This example assumes that one can only see in a straight line-of-sight. A mirror would allow you to see much farther. In fact, the sky, clouds, and sunlight can form a mirror, a meteorological phenomenon called refraction, and it is sometimes possible to see across Lake Michigan.*

Pingback: See a Double Sunset | Fun Facts From Charlie