Eiffel Tower !!!

Geometry Level 1

The tallest inhibited building in the world is the Eiffel Tower in Paris. If the observation tower is 30963 m above ground level, how far can a person standing in the observation tower see ( using a telescope ) ? Use 3960 miles for the radius of Earth. See Shuk's Diagram ( the figure below ). [ 1 miles = 1609.34 metre ] Your answer should be in the unit of metre ( m )


The answer is 628977.9.

Haqkiem Learner by Haqkiem Learner , 23, Malaysia

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2 solutions

Pranjal Jain
Dec 8, 2014

( R + h ) 2 = R 2 + x 2 (R+h)^{2}=R^{2}+x^{2}

x 2 = 2 h R + h 2 x^{2}=2hR+h^{2}

x = 2 h R + h 2 x=\sqrt{2hR+h^{2}} ⇒ x = 628977.9 m \Rightarrow x=\boxed{628977.9 m}

R=Radius of Earth (Assuming it is a sphere)

h=Height of tower

x=Length of tangent from top of tower on Earth

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Haqkiem Learner
Dec 8, 2014

Hint: Use Pythagoras Theorem by connecting the radius with the height of the tower and with the dotted lines that touches the surface of the earth...

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Mention that your answer is in metres

Pranjal Jain - 6 years, 6 months ago

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sorry im forgot to mention it on my question. But your calculation seems general. Do you get the exact answer as mine? im afraid that my answer is wrong, but i have check it a few times and i get the same answer...

Haqkiem Learner - 6 years, 6 months ago

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Yeah! Answer is exactly correct! Without any approximations. Just the unit was a mistake. Edit it or else it would be flagged.

Pranjal Jain - 6 years, 6 months ago

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@Pranjal Jain – Done !!! Btw, can you teach me how to use mathematical symbol in my problem ? Im using Daum Equation Editor, but after that when i paste it into my question it becomes a code form, not in the symbol form. How to do it?

Haqkiem Learner - 6 years, 6 months ago

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@Haqkiem Learner – image image

Pranjal Jain - 6 years, 6 months ago

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