I/D# 2: Unit O Concept 7-8

Inquiry Activity Summary

(http://upload.wikimedia.org/wikipedia/commons/6/68/30-60-90.svg)30-60-90º Triangle

1. In this 30-60-90º triangle the ratios that make up this triangle is literally 
1:2:3 that respectively measure 30-60-90º angles in this special right 
triangle. So, in this special right triangle we are given that that this is a 30-
60-90º and so basically what that means is how and why do we get the 
numbers that are on the left of you? Well, segment AD crosses down to segment CB and so what that does is that it creates a right triangle given 
that the angles are 30º, 60º, and 90º. But now how do we find the sides for 
each segment? In order to find √3 we must use the pythagorean theorem, a^2+b^2=c^2, and so what we plug in the pythagorean theorem is(segment DB) (1/2)^2, segment CD & CB were (1/2) so square it and you get 1. Next, we leave b^2 because we don't know what that is *hint hint (check out the pictures). Finally, c^2 means the hypotenuse (segment AB) is 2 because when we multiply "n" by 2 we manage to get the segments as you see on the right. "n" as you see in the 2nd picture is a variable that'll represent different types of problems when being applied to that number.

45-45-90º

2. "In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1 : 1 : 2, adding up to 180° or π radians. Hence, the angles respectively measure 45° (π/4), 45° (π/4), and 90° (π/2). The sides in this triangle are in the ratio 1 : 1 : √2, which follows immediately from the Pythagorean theorem." - Wikipedia. So first off what we should is cut the square diagonally and label your 45-45-90º since we can assume they are since the numbers are being given to us. To prove that the sides are 1, which also equal to "n" because "n" can be any number and basically it is a variable, we have to use the pythagorean theorem, which then later unlocks the true meaning of the hypotenuse. C=√2 because of the Pythagorean Theorem. The 45-45-90º is an easier triangle to decipher. 

Inquiry Activity Reflection1. “Something I never noticed before about special right triangles is…” that I could apply this to my mathematics test on Friday because the concept is somewhat complex. 2. “Being able to derive these patterns myself aids in my learning because…” I will be able to pass the test this Friday.