Hypotenuse 17 m, known leg 8 m
- b² = 17² − 8² = 289 − 64 = 225.
- b = √225 = 15 m.
- Check: 8² + 15² = 64 + 225 = 289 = 17².
Find a missing leg
Subtract square areas before taking the root.
The hypotenuse-square area is the total
Identify a missing leg, subtract the known leg square and take the nonnegative square root.
If c and one leg a are known, a² + b² = c² becomes b² = c² − a². Therefore b = √(c² − a²). You subtract because the hypotenuse-square area includes both leg-square areas. The known hypotenuse must be longer than the known leg.
Explore the relationship
Predict first. Change one value, then explain the result. Diagrams show the entered dimensions; displayed decimals are rounded.
Do not subtract lengths to find a side
For c = 13 and a = 5, b² = 169 − 25 = 144, giving b = 12. Subtracting lengths gives 13 − 5 = 8, which fails the check: 5² + 8² = 89, not 169. Rearrange the equation before pressing calculator buttons.
Check the geometry and the original equation
If the stated hypotenuse is shorter than a leg, the information is inconsistent with a right triangle. Equal hypotenuse and known-leg lengths would give a zero other leg, a degenerate shape. After solving, substitute into the original equation and confirm the missing leg is less than the hypotenuse.
Worked examples
Hypotenuse 10 cm, known leg 6 cm
- b = √(100 − 36) = √64 = 8 cm.
- 6, 8 and 10 satisfy the original relationship.
Guided Practice
A right triangle has hypotenuse 25 and one leg 24. Find the other leg.
A first hint
Subtract 24² from 25², not 24 from 25.
Compare your reasoning
b² = 625 − 576 = 49, so b = 7.
Practice
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Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Connections
A student labels 8 as the hypotenuse while another side is 10. Explain the contradiction before doing any calculation.
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