Step 1: Write the Formula
Use the Pythagorean Theorem.
a² + b² = c²
Formulas & graphing
Pythagorean Theorem
The Pythagorean Theorem helps us find a missing side of a right triangle. A right triangle has one 90-degree angle.
abc
a² + b² = c²
a and b are the legs.
c is the hypotenuse.
Why should I care?
The theorem helps measure diagonal distances in construction, navigation, screens, ramps, and sports fields.
Know the triangle
Find the Hypotenuse First
The hypotenuse is always across from the right angle. It is also the longest side. Label it c.
leg aleg bhypotenuse c
- The small square marks the right angle.
- The two sides touching the right angle are the legs.
- The side across from the right angle is the hypotenuse.
Worked example
Find the Hypotenuse When a = 3 and b = 4
Step 2: Substitute
Replace a and b with 3 and 4.
3² + 4² = c²
Step 3: Square and Add
3² = 9 and 4² = 16.
9 + 16 = 25
Step 4: Take the Square Root
The square root undoes the square.
c = √25 = 5
When a leg is missing
Subtract Instead of Add
Start
Known leg = 6
Hypotenuse = 10
a² + 6² = 10²
Square
Square the two known sides.
a² + 36 = 100
Subtract
Subtract 36 from 100.
a² = 100 − 36 = 64
Square Root
Find the positive square root.
a = √64 = 8
Try it
Pythagorean Theorem Calculator
Choose the missing side and follow the steps.
a² + b² = c²
3² + 4² = c²9 + 16 = c²25 = c²c = √25 = 5
Watch out
Common Mistakes
- Using the theorem on a triangle without a right angle.
- Labeling a leg as c. The hypotenuse must be c.
- Forgetting to take the square root at the end.
Memory tool
Find c Before You Calculate
Locate the right angle. The side across from it is c, the hypotenuse.
Your turn
10-Question Pythagorean Practice
Choose an answer or enter the missing side length.
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