Estimate the radius of the moon based on a solar eclipse given the distances between the earth and the moon, the earth and the sun, and the radius of the sun.

A diagram showing the moon directly between the earth and the sun is key here. If we call the radii of the sun and the moon r_s and r_m and the distances from earth D_s and D_m. respectively, there are similar triangles which can be analysed. the hypotenuse of both of the triangles is a straight line from earth tangential with both the moon and the sun, let the angle between this hypotenuse and the line of centres be 'a'. It is clear that tan(a) = r_s/D_s = r_m/D_m therefore r_m=D_m*r_s/D_s.