The Coming End of My Blog Investigation

The questions I have been investigating are I was researching are their any other angle combination's that show similar patters such as 30-60-90, 45-45-90? I have tried an angle combination which consist of 10 - 80 - 90. I have realized that this combination is not true because my data states that the hypotenus and long leg of the triangle are the same length. I know for a fact it is not true because the hypotenus is always the biggest side, no matter what the angle is. My suggestion for my next investigation is to remember the triangle formulas and the rule that carries with all the triangles.
My recent question that I have been trying to solve has not been solved yet. my question was, If you know the side lengths of a right triangle, can you predict what the angles will be? I dont know weather you could determine the angle if you only have the side legths. I know theirs a way but I dont know wat that way is.

How To Find the Angles of A Triangle When Only Given the Side's?

As I had said earlier, I am investigating If you know the side lengths of a right triangle, can you predict what the angles will be?

Through my data that I had collected, it seems that with the given sides I recieved they all form the same right triangle. I think this is true because these number are all multiples of each other.

Side AC	Side AB	Angle BAC	Side BC	Angle ABC
4	3	90°	5	53.13°	36.86°
8	6	90°	10	53.13°	36.86°
12	9	90°	15	53.13°	36.86°
16	12	90°	20	53.13°	36.86°

I am still investigating this qusetion because their is a way to get the angles if you are only given the sides. This question is important because it can end up in a standarized state test and i want the people to know how to solve this problem.

Side Combinations

Today I was researching are their any other angle combination's that show similar patters such as 30-60-90, 45-45-90?

Not only are angles important, but so are side combination's. An example of these side combination's are 3 - 4 - 5 right triangles. This is important because all of the sides are whole numbers. Also, the multiples of these numbers form right triangles with the same angles.

3^2 + 4^2=5^2 6^2 + 8^2 = 10^2
9 + 16 = 25 36 + 64 = 100
25 = 25 100 = 100

5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169

To follow through with my investigation, I will next investigate If you know the side lengths of a right triangle, can you predict what the angles will be?

What Are Special Right?

Special Right Triangles - its a short cut to find the missing sides of a right triangle.

ARE THEIR ANY OTHER ANGLE COMBINATION'S LIKE 45 - 45 -90 and 30 - 60 - 90?

Some angle combinations are a short cut to find the side length of a triangle easier and quicker. One angle combination is 45 - 45 - 90 where the hypotenuse is across the 90 degree angle and the 45 - 45 angles are across from the 2 congruent sides.

On a 45 - 45 - 90 triangle the Hypotenuse = xradical2 and the two legs are x

the other angle combination is 30 - 60 - 90 where the Hypotenuse is still across from the 90 degree angle. but the sides are not all congruent. The hypotenuse = 2x , The short side = x, The long side = xradical 3.

another combination i have dicroverd is 10 - 80 - 90. it has the same shap as 30 - 60 - 90 but different lengths. i wonder if they can have the same formula but it uses a smaller number.

Short Leg Long Leg Hypotenuse Angle A Angle B Angle C
0 0 0 10 0 80
.2 cm 1 cm 1 cm 10 90 80
.4 cm 2 cm 2 cm 10 90 80
.5 cm 3 cm 3 cm 10 90 80
.7 cm 4 cm 4 cm 10 90 80
.9 cm 5 cm 5 cm 10 90 80
1. cm 6 cm 6 cm 10 90 80


It seems like every whole number equals a multiple of 6. Like if I said that the Short Leg equals 5 the the Hypotenuse and Long Leg equals 30.

My equation is the SL = x, LL = 6x, H = 6x
When you plug these numbers in you will see that this could be another possible Special Right Triangle.

If you start 2cm then go up 6cm every time you get .4cm, 2.4cm, 3.4cm, 4.4cm.
You have to start at the Hypotenuse.