Pythagorean Theorem

Pythagorean Theorem

Pythagorean Theorem

 

 

Pythagorean Theorem

 

Right Angle Triange

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\(a^2 + b^2 = c^2\)
Pythagorean triple

3, 4, 5

5, 12, 13

8, 15, 17

7, 24, 25

20, 21, 29

Other Triangle

\(a^2 + b^2 > c^2\) → Acute Triangle

\(a^2 + b^2 < c^2\) → Obtuse Triangle

Example 01

Determine the length of AC from the picture below!

 

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AC is hypotenuse

\begin{equation*} \begin{split} \text{AC}^2& = \text{AB}^2 + \text{BC}^2\\\\ \text{AC}^2& =3^2 + 4^2\\\\ \text{AC}^2& =9 + 16 \\\\ \text{AC}^2& =25 \\\\ \text{AC}& = \sqrt{25}\\\\ \text{AC}& = \bbox[5px, border: 2px solid magenta] {5 \text{ cm}} \end{split} \end{equation*}


Example 02

Determine the length of BC from the picture below!

 

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AC is hypotenuse

\begin{equation*} \begin{split} \text{AC}^2& = \text{AB}^2 + \text{BC}^2\\\\ 17^2& =8^2 + \text{BC}^2\\\\ 289 & = 64 + \text{BC}^2\\\\ \text{BC}^2& =289 - 64 \\\\ \text{BC}^2& =225 \\\\ \text{BC}& = \sqrt{225}\\\\ \text{BC}& = \bbox[5px, border: 2px solid magenta] {15 \text{ cm}} \end{split} \end{equation*}


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