Finding the Hypotenuse
Ages 11–15Difficulty adapts to you
Finding the Hypotenuse
In a right-angled triangle, the longest side (opposite the right angle) is called the hypotenuse. The Pythagorean theorem says: a² + b² = c², where c is the hypotenuse.
Your goals
- ✓You can use a² + b² = c² to find the longest side of a right triangle.
- ✓You can use hypotenuse, Pythagorean theorem correctly.
- ✓You can label the hypotenuse before substituting values.
Words to know
- hypotenuse:
- The side opposite the right angle; it is the longest side of a right-angled triangle.
- Pythagorean theorem:
- For a right-angled triangle, a² + b² = c², where c is the hypotenuse.
Examples
- 1If a = 3 and b = 4: c² = 9 + 16 = 25, so c = 5.
- 2If a = 5 and b = 12: c² = 25 + 144 = 169, so c = 13.
More than one way to solve it
Try each method, then choose the one you can explain and check most clearly.
Method 1
Pythagorean equation
- 1.Label the shorter sides a and b.
- 2.Calculate a² + b².
- 3.Take the square root to find c.
Example: For sides 6 and 8: c = √(36 + 64) = √100 = 10.
Method 2
Known triples and scaling
- 1.Look for a known triple such as 3-4-5.
- 2.Find the scale factor.
- 3.Scale all three sides equally.
Example: 6-8-10 is the 3-4-5 triple multiplied by 2.
Check these
- • Do not use the theorem on a triangle that is not right-angled.
- • Keep every number, symbol, label, and unit in its correct place.
- • Choose the method that makes each step easiest to explain and check.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own finding the hypotenuse example, solve it, and explain how you checked it.
Professor Wise Owl
Wisdom & Understanding“Mistakes are proof that you are trying. Keep going!”