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Pythagoras of a Right Triangle
c² = a² + b²
Where: a = Pythagoras, b = b, c = hypotenuse
Use the same units for all lengths (e.g. all in cm); areas come out in cm², volumes in cm³.
Solved example
Given: b = 5, c = 10
Find: a (Pythagoras)
- Formula: c² = a² + b²
- Rearranged for a: a = √(-b² + c²)
- Substitute the values: a = √(10² - 5²)
- Rearranged for a: a = -√(-b² + c²)
- Substitute the values: a = -√(10² - 5²)
- Result: a = 8.660254 ; a = -8.660254
Answer: a = 8.660254
Calculator
How to calculate Pythagoras of a Right Triangle
- Write down the formula: c² = a² + b².
- Note the known values (b, c).
- Substitute them and simplify to find a.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Pythagoras of a Right Triangle?
The formula is c² = a² + b², where a = Pythagoras, b = b, c = hypotenuse.
What is Pythagoras of a Right Triangle when b = 5, c = 10?
a = 8.660254. Substitute the values into c² = a² + b² and simplify.