Determining Earth's circumference using shadows The problem is: Assuming the Sun is far away from Earth and that light rays are arriving parallel to each other, determine Earth’s circumference, assuming that it is spherical. Does anyone know how to solve this? Any hints or advice? I've been working some of the geometry but haven't gotten anything solid yet.

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The diagram shows the system you have. You can work out $\theta$ and $\phi$ with standard trigonometric methods. Then $\phi-\theta$ gives you an angle, and you have the arclength of 790km. This allows you to compute the radius of the earth, and thus the circumference using $2\pi r$.