Eratosthenes and the circumference of the earth
The small triangle with vertices Alexandria, Shadow and Top is not a right-angled triangle but you may assume it is (If the picture was to scale, the error from such an approximation would be less than any other error in the measurements).
1.Note that the angles β and γ are equal. Explain why.
2. Find the diameter of the circumference of the earth in terms of h and a, the two legs of the small triangle. (Hint: Start by finding R, the radius of the "green" circle above, in terms of a and h).
3. Why can we assume that the rays of the sun are parallel?