What are the angles of a 5/12/13 Triangle?

The diagram shows the angles of a 5/12/13 triangle. If you look at it carefully, you will notice that there are three sides with equal lengths.

These three sides have different lengths because they represent two different numbers. The first side represents number 1 and its length is 2 while the second side represents number 2 and its length is 4. Therefore, the third side represents number 3 and its length is 8. The diagram shows that these three sides are equal in all angles.

If you add up the lengths of each side, you get a total of 15. When you divide this total by three (3), you get the ratio 1:2:4 which equals 90 degrees.

You may remember from geometry class that when multiplying a ratio by itself, such as 1:2:4, it gives back to zero. Thus, the 90 degree angle is equal to the angle formed by adding together the two angles formed by the three sides.

You may wonder why there are only four sides. Why not five or six? Well, if you were to draw a circle around the triangle, then each of those circles would contain exactly one point.

So if you added up all points on any of those circles, you would get exactly one point on another circle. So, if you multiply 90 by 90, you get 0. This means that the angle between the top and bottom of the triangle is 45 degrees.

In addition to being a square, a circle has 360 degrees of a side. Thus, it makes sense that the angle between any two points on either side of a circle’s circumference is also 90 degrees.

Knowing these facts, you can now determine the values of all of the angles in a 5/12/13 triangle.

What are the equal sides of a 5/12/13 triangle?

There are only three possible values for the equal sides in a right triangle. These values are always in the ratio of 1:2: and they are expressed in a special way.

If you know any two of these values, then you can use simple algebra to solve for the third value.

The first step is to rewrite the ratio so that it contains only whole numbers. The two vertical angles are equal.

Each of these angles is 45 degrees. The two angles that lie on the horizontal line are also equal, and both of these angles are 30 degrees. If you add up all four of these angles, you get 180 degrees.

A 5/12/13 triangle is not a regular one since it contains irrational numbers. These irrational numbers tend to always have non-repeating and non-terminating decimals.

In the case of a 5/12/13 triangle, the ratio will equal 15:30:45. This is the same as 5:8:12.

The next step is to separate the three numbers into pairs. In this case, it will be 15 and 30 on one side and 8 and 12 on the other side.

You may notice that each side contains one larger number followed by a smaller number. For example, the square root of 2 is a irrational number since it can’t be written as a simple fraction. The square root of 2 can also be represented by the decimal . The square root of 3 can be represented by the decimal or . These decimals go on forever without ever repeating themselves.

In order to solve for the length of each side of a 5/12/13 triangle, you need to factor out a 5 and then a 13 from each fraction.

After separating these numbers, you can combine like terms on each side. On the left side, this means that 5 and 8 will combine to 45 and 15 and 30 will combine to 180.

The right side is already in the format of the original ratio, but with combined numbers.

You can now solve for a unknown value using the equation

a/(a + b) = c/(c + d). The square root of 5 can be expressed as or .

The square root of 13 can be expressed as or . You may notice that the denominators of these fractions are all divisible by 2. For example, is divisible by 2 and so is .

The square root of 5 can also be expressed as or . The square root of 13 can also be expressed as or .

You may notice that the denominators of these fractions are all divisible by 3.

In this case, a = 15, b = 8 and c = 12. The calculator will give you the decimal equivalent of a ratio.

This means that dividing 15 by 21 will give you 0.71. Dividing 30 by 35 gives you 0.91. When you add these two numbers together, you get 1.62. Since each side of the triangle is equal to this number, this must be the length of one side of the 5/12/13 triangle. For example, and are both divisible by 3.

You can use either of these to solve for a and c, but there is an easier method. The two denominators on the left side are both even numbers.

This means that all of the factors of 2 will divide evenly into each of the fractions on the left side. For example, 2 will divide into 45 and 180 with no remainder. In the same way, 3 will divide into 60 and 180 with no remainder. You can see that 2 and 3 combine to make 6, which is a factor of both 45 and 60.

This means that a is divisible by 6. Since c is the same fraction as b/a, c must be divisible by 6 as well.

In this case, a = 15 and c = 12. This means that 2 divides into each of the denominators on the left side.

This can be represented by saying that the least common multiple of 2 and 3, which can be represented by the variable M, will also divide evenly into each of the fractions on the left side. In this case, M = 2 × 3 = 6 and M will also divide into each of the denominators on the left side: 6 will divide into both 45 and 180 with no remainder.

Since b is 8, this means that b and c are both divisible by 2, but a isn’t.

Since a and c are both divisible by 6, you can also say that a/6 and c/6 are both divisible by 2 and 3.

__Sources & references used in this article:__

- A Classroom Note on Generating Examples for the Laws of Sines and Cosines From Pythagorean Triangles (L Sher, D Sher – Mathematics and Computer Education, 2007 – search.proquest.com)

http://search.proquest.com/openview/3cf203adf7c5b4ddf058386e58ff4243/1?pq-origsite=gscholar&cbl=35418 - Hero triangles (LE Ellis – The Mathematical Gazette, 2002 – cambridge.org)

https://www.cambridge.org/core/journals/mathematical-gazette/article/hero-triangles/4D2604554AC4DE609579CAF608417A2E - A possible Pythagorean triangle at Stonehenge (WE Dibble – Journal for the History of Astronomy, 1976 – search.proquest.com)

http://search.proquest.com/openview/0b6ad24ac1ad193a8f9e1bc33bb8a291/1?pq-origsite=gscholar&cbl=1818157 - The remarkable incircle of a triangle (I Fine, TJ Osler – Mathematics and Computer Education, 2001 – Citeseer)

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.539.3179&rep=rep1&type=pdf - 87.23 Triangles with a 60° angle and sides of integer length (B Burn – The Mathematical Gazette, 2003 – JSTOR)

https://www.jstor.org/stable/3620591 - Pythagoras Triples Explained via Central Squares. (LT Gomes – Australian Senior Mathematics Journal, 2015 – ERIC)

https://eric.ed.gov/?id=EJ1093370 - The Ubaid Period: Evidence of Architectural Planning and the Use of a Standard Unit of Measurement-the” Ubaid cubit” in Mesopotamia (S KUBBA – Paléorient, 1990 – JSTOR)

https://www.jstor.org/stable/41492401