How To Find C Squared In Pythagorean Theorem

Pythagorean theorem

The Pythagorean Theorem was named later on famous Greek mathematician Pythagoras.

It is an important formula that states the following: a² + b² = c^two

The 2d effigy below helps us to see why the formula works.

Did you make the following important observation? The figure below may help!

Notice that the red square has ii triangles in information technology and the blue square has also ii triangles in it.

The blackness square has 4 of the same triangle in information technology.

Pythagorean theorem

Therefore, expanse of red square + surface area of blueish square = surface area of black square

Let a = the length of a side of the red square

Allow b = the length of a side of the bluish square

Allow c = the length of a side of the black foursquare

Therefore, aⁱⁱ + b² = cⁱⁱ

Pythagorean theorem

Mostly speaking, in any correct triangle, allow c exist the length of the longest side (called hypotenuse) and let a and b be the length of the other two sides (chosen legs).

Right triangle

The theorem states that the length of the hypotenuse squared is equal to the length of side a squared plus the length of side b squared. Written as an equation, c^two = a² + b²

Thus, given two sides, the third side can be found using the formula.

Nosotros volition illustrate with examples, but earlier proceeding, you lot should know How to notice the foursquare root of a number and how to solve equations using subtraction

Do #1

Let a = 3 and b = 4. Find c, or the longest side

c² = a² + bⁱⁱ

c² = 3² + 4²

c²= nine + 16

c² = 25

c = √25

The sign (√) means square root

c = 5

Practise #2

Let c = 10 and a = 8. Find b, or the other leg.

c^two = a^two + b²

10² = 8² + bⁱⁱ

100 = 64 + b²

100 - 64 = 64 - 64 + b² (minus 64 from both sides to isolate bⁱⁱ )

36 = 0 + b²

36 = b²

b = √36 = vi

Practise #three

Let c = thirteen and b = 5. Find a

c² = a ²+ b²

13² = a² + 5ⁱⁱ

169 = a² + 25

169 - 25 = a² + 25-25

144 = a² + 0

144 = a²

a = √144 = 12

Have the Pythagorean theorem quiz below to see how well you understand this lesson.

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