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How to Find a Sun Angle

While many people believe that the sun is directly above them at noon, this is only true on some parts of the planet on any given day. The Earth's rotational axis is tilted by an angle of 23.4 degrees. Throughout the Earth's orbit around the sun, different parts of the planet move closer to the sun during different times of the year. Anyone standing north of the Tropic of Cancer will always find the sun in the southern sky, anyone standing south of the Tropic of Capricorn will always find the sun in the northern sky. Although the sun is in a different position every day, it is easy to calculate the angle of sun rays, using a little ingenuity and some simple trigonometry.

Things You'll Need

2 meter sticks
Paper
Pencil
Calculator

Instructions

- 1
  Take one of the meter sticks to a sunny spot outside and stand it straight up. Dig a small hole and place the stick in it, filling the hole with dirt to ensure the meter stick stands erect.
- 2
  Measure the height of the meter stick from the ground where the shadow of the meter stick begins. Record this number for use in Step 4.
- 3
  Measure the length of the shadow created by the meter stick. Measure from the bottom of the meter stick to the end of the shadow. Record this number for use in Step 4.
- 4
  Divide the length of the shadow from Step 3 by the length of the meter stick from Step 2. Take the inverse sine, or arcsine, of the number you just found. The resulting value is the angle light is traveling with respect to the perpendicular, but it is expressed in radians rather than degrees.
- 5
  Multiply the number found in Step 4 by 180, then divide the resulting value by the constant pi. Now you have converted the angle from radians to degrees.

Astronomy