A long time ago (more than 2500 years), a Greek mathematician named Pythagoras (570-495 BC) discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse. This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem.
The longest side of a Right Angle Triangle is called the "HYPOTENUSE".
The sum of square of each of the other 2 sides is always equal to the square of the hypotenuse (c).
i.e. a^{2} + b^{2} = C^{2}
Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles:
Pythagoras theorem - ideal maths lab with models and projects (YouTube)
Pythagorean Theorem Puzzle (Flash)
Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
5 cm
Another Example: Find the unknown hypotenuse with the sides (legs) 12 cm and 5 cm long.
c^{2} = a^{2} + b^{2}
⇒ c^{2} = 5^{2 }+ 12^{2}
⇒ c^{2} =25 + 144
⇒ c^{2} = 169
⇒ c = √ 169
⇒ c = 13 cm
Still applying the Formula: a^{2} + b^{2} = C^{2}
Transform the formula: ⇒ a^{2} = C^{2 }- b^{2}
Example:
Evaluating the Hypotenuse with Pythagoras' Theorem by Eddie Woo (YouTube)
Evaluating Side Lengths w/ Pythagoras' Theorem by Eddie Woo (YouTube)
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".
Pythagoras, Pythagorean Thereom, Right-angled Triangle, Hypothenuse, Side, Leg, Pythagorean triple, Converse, Trigonometry, Geometry, Primitive triple, Square, Square root
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