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Pythagorean triples. The most famous example of a Pythagorean triple is the (3, 4, 5) triangle: In this case, the hypotenuse has length 5, and the other two sides have length 3 and 4. 3 squared is 9, 4 squared is 16, which adds up to 25. And, of course, 5 squared is also equal to 25. Another example is the (5, 12, 13) triangle:
- Triangles
- List of The First Few
- Scale Them Up
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When a triangle's sides are a Pythagorean Triple it is a right angled triangle. See Pythagoras' Theoremfor more details. Here are two more Pythagorean Triples: And each triangle has a right angle!
Here is a list of the first few Pythagorean Triples (notincluding "scaled up" versions mentioned below):
The simplest way to create further Pythagorean Triples is to scale up a set of triples. If you want to know more about them read Pythagorean Triples - Advanced
We can use these triples to make a right angle in the real world (such as with carpentry, tiling, etc) The simple (3,4,5 triple)is the easiest to remember. And if you need a triple with two nearly equalsides use (119,120,169) or (696,697,985).
It is easy to construct sets of Pythagorean Triples. When m and n are any two positive integers (m > n): a = m 2 − n 2. b = 2mn. c = m 2 + n 2. Then a, b and c form a Pythagorean Triple. This is known as "Euclid's formula". Example: m=2 and n=1. a = 2 2 − 1 2 = 4 − 1 = 3.
Angle-based special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degrees or π 2 radians, is equal to the sum of the other two angles. The side lengths are generally deduced from the basis of the unit ...
A 3-4-5 right triangle is a triangle whose side lengths are in the ratio of 3:4:5. In other words, a 3-4-5 triangle has the ratio of the sides in whole numbers called Pythagorean Triples. This ratio can be given as: Side 1: Side 2: Hypotenuse = 3n: 4n: 5n = 3: 4: 5. We can prove this by using the Pythagorean Theorem as follows: ⇒ a 2 + b 2 = c 2.
It is perhaps surprising that there are some right-angled triangles where all three sides are whole numbers called Pythagorean Triangles. The three whole number side-lengths are called a Pythagorean triple or triad. An example is a = 3, b = 4 and h = 5, called "the 3-4-5 triangle".
People also ask
Why is the 3 4 5 triangle called a primary Pythagorean triple?
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Apr 5, 2012 · The Pythagorean Theorem is: {eq}a^2 + b^2 = c^2 {/eq}. The 3-4-5 triangle method provides a way to check and create other right triangles using proportional side lengths to the constant ratio 3:4: ...
