The Leaning Tower of Pisa is 55.863 m tall and leans 3.9 m from the perpendicular, as shown below. The tower of the Suurhusen Church in north-western Germany is 27.37 m tall and leans 2.47 m from the perpendicular. By providing diagrams and suitable calculations and explanations, decide which tower should enter the Guinness Book of Records as the Most Tilted Tower in the World.

Junior Cycle Mathematics Trigonometry: The Leaning Tower of Pisa is 55.

The Leaning Tower of Pisa is 55.863 m tall and leans 3.9 m from the perpendicular, as shown below - Junior Cycle Mathematics - Question 16 - 2014

Question 16

The Leaning Tower of Pisa is 55.863 m tall and leans 3.9 m from the perpendicular, as shown below. The tower of the Suurhusen Church in north-western Germany is 27.3... show full transcript

Worked Solution & Example Answer:The Leaning Tower of Pisa is 55.863 m tall and leans 3.9 m from the perpendicular, as shown below - Junior Cycle Mathematics - Question 16 - 2014

Step 1

Calculate the angle of tilt for the Leaning Tower of Pisa

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Answer

To find the angle of tilt, we can use the cosine function:

ext{cos}(y) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3.9}{55.863} \approx 0.0698

Using the inverse cosine to find the angle:

\begin{align*} y & = \cos^{-1}(0.0698)\ & \approx 85.9967^{\circ} \end{align*}

Step 2

Calculate the angle of tilt for the Suurhusen Church

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Answer

Using the same approach for the Suurhusen Church:

ext{cos}(y) = \frac{2.47}{27.37} \approx 0.09024

Finding the angle:

\begin{align*} y & = \cos^{-1}(0.09024)\ & \approx 84.8223^{\circ} \end{align*}

Step 3

Compare the angles to determine which tower is more tilted

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Answer

The angles calculated are approximately:

Leaning Tower of Pisa: $85.9967^{\circ}$
Suurhusen Church: $84.8223^{\circ}$

Since the angle for the Suurhusen Church is smaller than that of the Leaning Tower of Pisa, it should be recognized as the Most Tilted Tower in the World.

The Leaning Tower of Pisa is 55.863 m tall and leans 3.9 m from the perpendicular, as shown below - Junior Cycle Mathematics - Question 16 - 2014

Worked Solution & Example Answer:The Leaning Tower of Pisa is 55.863 m tall and leans 3.9 m from the perpendicular, as shown below - Junior Cycle Mathematics - Question 16 - 2014

Calculate the angle of tilt for the Leaning Tower of Pisa

Calculate the angle of tilt for the Suurhusen Church

Compare the angles to determine which tower is more tilted

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