You are an astronomer on planet tirth, which orbits a distant star. it has recently been accepted that tirth is spherical in shape, though no one knows its size. one day, you learn that on the equinox your sun is directly overhead in the city of tyene, located 750 kilometers due north of you. on the equinox, you go outside in alectown and observe that the altitude of your sun is 87.0 ∘.

As you should be directly south of Tyene, this same angular distance among both yourself as well as the town of Tyene seems to be the distinction to be made throughout the height including its sun at two positions on a specified day.

The sun is therefore immediately overhead in Tyene, does have an altitude with respect to the horizon will be:

⇒ [tex]\Theta_r = 90^{\circ}[/tex]

At the very same day on yourself location, the altitude of the sun will be:

⇒ [tex]\Theta_A=85^{\circ}[/tex]

Therefore, a complete circle is 360 degrees. So the angular distinction will be somewhere between you as well as Tyene:

⇒ [tex]\frac{5}{360}[/tex]

Therefore,

⇒ [tex]\frac{\Theta}{x}=\frac{360}{Circumference}[/tex]

⇒ [tex]Circumference=\frac{360}{\Theta}\times x[/tex]

If, [tex]\Theta = 5^{\circ}[/tex]

[tex]x (separation) = 600 \ km[/tex]

Now,

The circumference = [tex]\frac{360}{5}\times 600[/tex]

= [tex]43,200 \ km[/tex]