Pythagorean Theorem Guide: Formula and Examples
Use a^2 + b^2 = c^2 to solve right-triangle side lengths. This guide keeps the math practical, so you can understand what to enter, why it works, and how to spot an answer that does not make sense.
Quick Answer
The Pythagorean theorem works only for right triangles. The longest side is the hypotenuse, usually called c.
Identify the right angle.When to Use This
This topic is useful when a problem looks familiar, but you are not sure which button, formula, or order of steps to use. Start by naming the goal in normal words, then translate it into the calculator setup.
- measuring rooms, boxes, and shapes
- checking whether units are square or cubic
- right-triangle and construction problems
Step-by-Step Method
- Identify the right angle.
- Label the two legs a and b.
- Put the longest side as c.
- Square, add or subtract, then take the square root.
After you get the answer, do one quick reasonableness check. Ask whether the answer should be bigger or smaller than the starting number, whether the unit is correct, and whether a rounded answer is acceptable.
Calculator Tips
- Sketch the shape before choosing a formula.
- Write units next to every measurement.
- Square units are for area; cubic units are for volume.
Worked Example
Work slowly through the steps, then check the answer by reversing the operation or estimating the size.
Common Mistakes
Pause and check this before trusting the final answer. A small setup mistake can make the calculator look wrong even when it only followed the input.
Pause and check this before trusting the final answer. A small setup mistake can make the calculator look wrong even when it only followed the input.
FAQ
Can I use a calculator for this?
Yes. A calculator helps with arithmetic, but the important part is choosing the right formula and entering the values in the right places.
How should I check my answer?
Estimate first, then substitute the answer back into the problem or reverse the operation. If the result is wildly larger or smaller than expected, recheck the setup.