Inquiry Activity
1. Deriving a 45-45-90 triangle
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2. Deriving a 30-60-90 triangle
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3. The reason why both of these the 30-6-90 triangle and the 45-45-90 triangle have variables of "n" and not just the numbers because there is a relationship between as to why these numbers are there and they end up being a patter for all triangles of that kind. The variables make it a rule and make it true for all the special right triangles.
Inquiry Activity Reflection
1.Something I never noticed about special right triangles is... that all the sides have a pattern that is common between that type of right triangle. For example, In a 45-45-90 triangle we know that "a" and "b" will be the same since they have the same angle value. The hypotenuse however has an extra radical 2 being multiplied to the value of both "a" and "b". For a 30-60-90 triangle we see that the length of the shortest side which could be classified as "a" has a value of n. The value of the medium size side is n radical 3, and the side of the hypotenuse is 2n. Which makes since we see that the hypotenuse is suppose to be greater since it is the longest side and it is in the equation.
2. Being able to derive these patterns myself aid in my learning because... it helps me understand how everything connects and allows me to fully understand how to solve each and every problem. This can be very important to me in the long run because if i ever forget the rules i can easily derive them using the Pythagorean theorem and will help me connect everything else to the unit circle and not just with a radius (hypotenuse) of 1 but of any number and can solve it.
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