5th blog [FINAL]

Alright everybody!today is the last and final blog i am making. so thank you for reading my blog and i hope you know all things we had learned.so for the final question i will be investigating is if two of the side length are double or triple what will be the angle and the pattern of the hypotenuse.
if you remember what happen in the last blog, like when the two side are the same what will be the angle. its the same thing but a little different and i will tell you why. so when the side length are double angle B is always 27 degree and angle C is always 63 degree and the hypotenuse goes by the square root of 5 and it will be a 27-68-90 triangle. When the side are triple angle B is always 18 degree and angle C is always 72 degree and the hypotenuse pattern goes by the square root of 10 and it will be a 18-72-90 triangle. the way i founded this investigation out is that i went on some sites about triangle and make my own triangle i did some data until i have a pattern which i did. then i wrote them down and make a table which you see below.

4.47

Side 1	Side 2	Hypotenuse	Angle B	Angle c
2	4	27	63
3	6	6.71	27	63
4	8	8.94	27	63
5	10	11.18	27	63
6	12	13.42	27	63

6.32

Side 1	Side 2	Hypotenuse	Angle B	Angle c
2	6	18	72
3	9	9.49	18	72
4	12	12.65	18	72
5	15	15.81	18	72
6	18	18.97	18	72

i want to go up to the quadruplet table but i don't have much time to do that. so the angle b decrease and stay the same number even though the side doubled or triple or quadruplet and etc. and so will angle C and it will increase as much when the side is getting bigger.also the hypotenuse increase by the square root of 5 when the side get higher. so for the next question for you is if all the side length change into different measurement what will happen to the angle?

4th blog

Okay then!we already know that in a right triangle the angle a is 90 degree because it's a right angle. Also on angle b the angle decrease each time the side length change, and on angle c it increase each time triangle change too. Oh Yeah! we also talk about what was the angle if it wasn't a right triangle but it was the same pattern as the right triangle. so now we are going to talk about what will be the angle if the two side length are the same. do you think the pattern will be the same or will it change this time?
If you said its the same...you are...WRONG! well when the two side are the same the hypotenuse's size is bigger then the other two side by root of two and the two angle are the same, they are always 45 degree angle. so it is really a 45-45-90 triangle. Weird right! So if you don't believe me look at this.
1.41

Side 1	Side 2	Hypotenuse	Angle B	Angle c
1	1	45	45
2	2	2.83	45	45
3	3	4.24	45	45
4	4	5.66	45	45
5	5	7.07	45	45

There a clue I'm going to tell if you subtract two of the measurement in the hypotenuse row like 2.83-1.41 it equal to 1.42,and 1.42 or 1.41 also mean the same thing as root 2. so this prove that it is a 45-45-90 triangle when the side is the same length. so next investigation i will be doing is if two of the side side length are double of triple what will be the angles and hypotenuse?

third blog

the question i am investigating is if it wasn't a right triangle will the angle change or will be the same. the way i am going to do this is to find more data and see the patterns of the data i have collected.
what i found is its the same thing angle b still decrease and angle c increase in a triangle that is not 90 degree. but what i think the angle will never change it's pattern. so the next question i will answer soon is if two of the side length is the same what will be the angles.

here are all the data i did in the investigation.
DATA 1:
Side 1 Side 2 Hypotenuse Angle B Angle C
1 1 1.41 45 45
1 2 2.24 27 63
1 3 3.16 18 72
1 4 4.12 14 76
1 5 5.10 11 79
1 6 6.10 9 81
1 7 7.10 8 82


DATA 2:
Side 1 Side 2 Hypotenuse Angle B Angle C
2 1 2.24 63 27
2 2 2.83 45 45
2 3 3.61 34 56
2 4 4.47 27 63
2 5 5.39 22 68

DATA 3:
Side 1 Side 2 Hypotenuse Angle B Angle C
1 2 2.24 63 27
1 4 4.12 14 76
1 6 6.10 9 81
1 8 8.10 7 83
1 10 10.04 6 84

what i said before was correct because i went and find many new data to prove my answer was right.what i did is that i went on some sites and found many right triangle
and change many sides and found all angle to it.

if you know the side length of a right triangle how will you know the angles? This is the investigation which i will be solving now. okay. i hope you already know that to find the side in a right triangle which you have to use the Pythagorean Therom, the equation of that is a2+b2=c2. side a is the short leg and side b is the long leg. Also side c is the hypotenuse of the traingle.
now that you know how to find side of the of the triangle. but the real question is to find the angles of the right triangle when you know the side. it's not easy to find it but you already know that one of the angle is always 90 degree so we already find one of the angles. but what about the other two angles? well, if you keep the 90 degree and one of the side the same and change other side how will the angles change. for example side one is one and it will always be the same length. but in side two it will always change like one centimeter and two centimeter and three and so on and so forth. in that data the hypotenuse is getting bigger and bigger. so in angle b it's getting smaller and in angle c it's getting so big each time the the side change.
so the answer of this investigation is that each time the side change in a right triangle the angle a will always be 90 but angle b will become smaller and angle c will become bigger .