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With the current restoration, engineers now think the tower can stand for another 200 years

The math behind it

(58.36)^2 = (5.45)^2 + b^2

b=58.10

COS B = 5.44/58.36

(75)^2+(58.10)^2= C^2

<B = 84.65

C=94.87

<a = 180-84.65-90

COS <unknown= 75/94.87

<a= 5.35

<unknown= 37.76

Background

More background

The tower was built back in 1173 with marble, so the assumptions of modern engineering don’t really apply. Not long after it was built, the ground under one side started to sink under the weight of the stones. Workers tried to fix it by making the columns on the other side slightly bigger to even out the lean. But that didn’t work.

The structure continued to decline into the 20th century, when engineers realized they had a problem. The tower was leaning more, about 1/20th of an inch every year, which would increase as the tower’s center of gravity shifted. Eventually, it would simply fall. People tried to restore it and eventually after many years of cables and cement they reduced the leaning by 17 inches.

Math Part of the Tower

In terms of angles, the tower now leans at 3.99 degrees. Considering the weight and height of the tower, physicists have said the maximum angle would be 5.45 degrees before the tower falls (at its worst, the tower once leaned at 5.5 degrees. Everyone is still surprised that it didn’t collapse).

The leaning tower of Pisa in Italy leans because it was built on unstable soil. The tower is approximately 58.36m tall from its foundation. The top of the tower leans about 5.45 m off center. d=75m

Trigonometry behind the Leaning Tower of Pisa

By: Amelia Gabriel and Emily White

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