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The light from the sun travels in a straight line, and we can assume the light rays to be parellel. The angle of incidence on the earths rounded surface depends on where you are on the earth and what time it is. Mid-day on the equator and the rays would hit the ground straight on. Further to the north or south, or later/earlier in the day and the light rays would hit at more of angle. The rays would also have to penitrate more of the earths atmosphere as the angle increases, which takes more `strength` out of the sun.
The plane upon which the Earth travels round the Sun is called the ecliptic. It is only when two bodies are on this plane, and in line with the Sun, that an eclipse is observed. Hence the name ecliptic. The Earth's spin axis is always oriented about 23.4 degrees from the ecliptic plane. The Earth's spin axis is never perpendicular to the Sun's rays. You may be referring to the Sun being directly overhead at the Equator twice per year.
The angle of the sun can be worked out through trigonometry, but first you will need the height of the object that is causing the shadow, since a taller object will make a longer shadow. Tan a = H/2.44 Where a is the angle and H is the height of the object. And the date is not relevant.
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