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The Eiffel Tower in Paris, France. Lizbeth is 5.5 feet tall. She looks up at an angle of elevation of 72° to see the top from 318 feet away. Based on her measurements, calculate the height of the Eiffel Tower. Round to the nearest hundredth of a foot.

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Answer:

The height of the Eiffel Tower will be 318 feet.

Step-by-step explanation:

Please check the attached graph.

From the diagram, it is clear that Lizbeth is 5.5 ft tall, seeing the top from 318 feet away, making an angle of elevation to be 72⁰.

The diagram makes a right-angled triangle.

  • Given the angle = Ф = 72⁰
  • Adjacent = a = 5.5 ft
  • Opposite = b = 318 ft
  • Hypotenuse = the height of the Eiffel Tower = c ?

Pythagorean Theorem:

For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as:

[tex]c=\sqrt{a^2+b^2}[/tex]

  • [tex]a=5.5[/tex]
  • [tex]b=318[/tex]

[tex]c=\sqrt{5.5^2+318^2}[/tex]

[tex]c=318[/tex] feet

Therefore, the height of the Eiffel Tower will be 318 feet.

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