Right Triangles & the Pythagorean Theorem (Grade 8)
In a right triangle (one 90° angle), the two short sides (legs) and the longest side (hypotenuse, opposite the right angle) are linked by the Pythagorean theorem: leg² + leg² = hypotenuse², or a² + b² = c².
Understanding right triangles & the pythagorean theorem
So if the legs are 3 and 4, the hypotenuse is √(9 + 16) = √25 = 5. It only works for right triangles.
Seeing it in action
Worked example
A right triangle has legs 3 and 4. Find the hypotenuse.
a² + b² = c²: 3² + 4² = 9 + 16 = 25. c = √25 = 5.
For right triangles, a² + b² = c².
A common mistake, and the fix
Adding the legs instead of their squares, or using the rule without a right angle.
With legs 3 and 4, 3 + 4 = 7 is too long; square, add, then take the root: 9 + 16 = 25 and √25 = 5. The hypotenuse is always the longest side, so a result shorter than a leg is a warning sign.
Try a few
Legs 6 and 8 — hypotenuse?
36 + 64 = 100.
Legs 5 and 12 — hypotenuse?
25 + 144 = 169.
Legs 9 and 12 — hypotenuse?
81 + 144 = 225.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
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