📖Definition
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides.
📐Formula
Where a and b are the lengths of the two legs (shorter sides), and c is the length of the hypotenuse (the longest side, opposite the right angle).
📝Step-by-Step Guide
Identify the sides
Determine which side is the hypotenuse (opposite the right angle) and which are the legs.
Set up the equation
Use a² + b² = c² with the known values.
Solve for the unknown
If finding the hypotenuse: c = √(a² + b²). If finding a leg: a = √(c² - b²).
Calculate and check
Compute the final value and verify your answer makes sense geometrically.
⚠️Common Mistakes to Avoid
- Confusing the hypotenuse with a leg
- Forgetting to take the square root at the end
- Using the formula for non-right triangles
- Calculation errors when squaring numbers
✏️Practice Problems
Find the hypotenuse when a = 3 and b = 4
Answer: c = 5
Find side b when a = 5 and c = 13
Answer: b = 12
A ladder is 10m long and leans against a wall, reaching 8m high. How far from the wall is the base?
Answer: 6 meters
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