Answer:
6000 miles
Explanation:
The angle of the sun shone at an angle of 30° to the zenith
This means that the angle of the sector of the circle is 30° (θ)
S = Length of the sector of the circle = 500 miles (Distance between Alexandria and Syene)
r = radius of earth
Converting 30° to radians
[tex]\theta=30\times\frac{\pi}{180}[/tex]
[tex]S=r\theta\\\Rightarrow r=\frac{S}{\theta}\\\Rightarrow r=\frac{500}{30\times\frac{\pi}{180}}\\\Rightarrow r=954.93\ Miles[/tex]
Circumference
[tex]C=2\pi r\\\Rightarrow C=2\pi \frac{500}{30\times\frac{\pi}{180}}\\\Rightarrow C=6000\ Miles[/tex]
∴ Earth’s circumference would have been 6000 miles
