Explanation
The Pythagorean Theorem is used to find a missing side in a right triangle (a triangle with a \(90^\circ\) angle).
If we know the lengths of two sides, we can find the third side.
Formula / Rule
\(a^2 + b^2 = c^2\)
Where:
- \(c\) is the hypotenuse (the longest side, opposite the \(90^\circ\) angle)
- \(a\) and \(b\) are the other two sides
Example
Find the hypotenuse \(c\) of a right triangle with sides \(a=3\) and \(b=1\).
Step 1: Substitute the values into the formula
\(3^2 + 1^2 = c^2\)
Step 2: Simplify the squares
\(9 + 1 = c^2\)
Step 3: Add the numbers
\(10 = c^2\)
Step 4: Rewrite the equation
c² = 10
Step 5: Take the square root of both sides
\(c = \sqrt{10}\)
Since length is always positive, we take the positive value
Final Answer:
\(c = \sqrt{10}\)
Video Explanation
Practice
Continue Learning
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