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When the angle of the sun above the horizon is 45 degrees, then an error in measuring its altitude leads to the smallest error in calculating an object's size by measuring the length of its shadow.

So, if you are located in a place where it's possible for the sun to appear 45 degrees above the horizon at any time of day, then that's the time of day when such a calculation is most accurate.

If you're located in a place where it's neverpossible for the sun to appear 45 degrees above the horizon at any time of day, then the best time would be the time when the sun is as high as possible in the sky. That's local solar Noon.

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