The sun on the hottest day of the year gets to just about 23 degrees latitude above the equator. Eretz Yisroel is about 34 degrees north. That means that the sun is always at least on an 11 degree angle coming down over Eretz Yisroel.
According to one shitta in the Gemara in Sukkah, a Sukkah that is more than 20 amos high is only pasul when the width and length are both just 7 tefachim - because then the shade is coming from the walls. But in a sukkah that is larger than 7x7, you can make it higher than 20 amos because the shade will come from the sechach.
But if you figure 11 degrees of angle on the sunlight, and to commutate using sin cos and tan, you will see that in a 7x7 sukkah the sunlight coming on 11 degrees will only make it about 8 amos down the wall, not nearly the 20 amos needed?
And that, my students, is why you need to know trigonometry.
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