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

Answer-

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,

$\Rightarrow\cos \theta=\dfrac{OB}{OA}\\\\\Rightarrow \theta=\cos^{-1}\dfrac{OB}{OA}\\\\\Rightarrow \theta=\cos^{-1}\dfrac{6240}{6240.3}\\\\\Rightarrow \theta=0.562$

So,

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

So, the arc length will be,

$=\dfrac{0.562}{360}\times 39207\\\\=61.21\ km$

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