Question

From how far on a clear day, and assuming there are no obstructions, could you see from the top of the Eiffel Tower? Take the height of the Eiffel Tower as 300 m and the radius of the earth as 6240 km.

Answer 1

From 61.21 km on a clear day you could see from the top of the Eiffel Tower.

Solution-

From the attachment,

OA = Distance between the top of the Eiffel Tower and center of the earth = 6240 km + 300 m = 6240 km + 0.300 km = 6240.3 km

OB = Radius of the earth = 6240 km

Applying trigonometric properties,

`\Rightarrow\cos \theta=(OB)/(OA)\\\\\Rightarrow \theta=\cos^(-1)(OB)/(OA)\\\\\Rightarrow \theta=\cos^(-1)(6240)/(6240.3)\\\\\Rightarrow \theta=0.562`

So,

`\text{Circumference of the earth} = 2\pi * radius = 2\pi * 6240=12480\pi=39207 km`

So, the arc length will be,

`=(0.562)/(360)* 39207\\\\=61.21\ km`

Therefore, from 61.21 km on a clear day you could see from the top of the Eiffel Tower.