This is the 30-60-90 triangle. As you can see i have drawn out the triangle and cut it in half making it a 30-60-90 triangle. each side of the triangle is 1 but after cutting it side c stays the same side a is 1/2 and side b is unknown. That's what we are trying to find. So we will use the Pythagorean theorem so solve for the side b. as seen in my work b is radical 3/2.
This is a 45-45-90 triangle. As you can see i cut a square in half diagonally. Doing this i made the spacial right triangle. A all of the sides of the square are 1 so cutting it in 2 changes it. Side A and side B are both equal to 1. angle C is the unknown one so that what we will be looking for using the Pythagorean theorem . In my work after i solved for C it is radical 2.
The N in front of each number like in the 30-60-90 triangle is just a variable in front of each side length so show that all it is is a ratio. so that it doesn't really matter how big or small it is as long as it follows the ratio it is one of the two special right triangle.
Being able to derive these patterns myself aids in my learning because it shows me how each ratio was originally derived from and that it make me memorize the concept more.
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