Question!

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[Originally posted in Discussions]
I know this has been posted before but I still don't get this:
Why are the small side lengths on that little triangle related to 3/2 and everything? 
The triangle in the diagram is a 306090 right triangle, which you can think of as being an equilateral triangle cut in half! (An equilateral triangle has three angles that are all equal to 60 degrees and all three sides the same length, so the equilateral triangle would have three sides of length 3.) The side of this 306090 triangle that has length 3/2 came from cutting one of the equilateral triangle's sides in half. Now, for the third side, we can get that by using the Pythagorean Theorem, which was covered in Day 1 of Module 0. This theorem says that if you take the hypotenuse length and square it, that should equal (3/2)² + ( other leg )². Then we can solve for the other leg, which has length
$$ \frac{3}{2} \sqrt{3} $$
Happy Learning!
The Daily Challenge Team

Hold up how did you get 3/2 sqrt 3?

@TheBladeDancer (long leg)^2 = (3^2)  (3 / 2)^2 which simplifies to 3/2√3