



 
I David, I copied Penny's diagram from her response to a similar question.
P is the top of the bluff, C is the centre of the Earth and H is a point on the horizon for someone standing at P. The radius of the Earth is about 3963 miles and 200 feet is 200/5280 miles so the length of CH, CH, is 3963 miles and the length of PC, PC, is (3963 + 200/5280) miles. The angle CHP is a right angle so we can use Pythagoras theorem which says
or
Solving for HP I get HP = 17.3 miles. I then repeated the calculation, this time with P the top of the Willis Tower and got
In this case HP = 49.8 miles. Thus someone at the top of the bluff can see over the horizon to the top of the tower as long as the bluff and the tower are less the 17.3 + 49.8 = 67.1 miles apart. I then went to Google Maps and asked for a route from St. Joseph to the Willis Tower and used the scale to estimate the distance, "as the crow flies". (I cut and pasted the scale below.) From the map my estimate of the distance is 63 miles. So who is right? It's quite close. You probably have a better idea of the distance from the bluff to the tower. Harley
 


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