How it’s calculated
In a right triangle the two legs a and b meet at 90°, and the hypotenuse c is the side opposite the right angle. The Pythagorean theorem links them, and the acute angles come from the tangent ratio.
Example: legs 3 ft and 4 ft give c = √(9 + 16) = √25 = 5 ft, α = arctan(0.75) ≈ 36.87°, β ≈ 53.13°, area 6 ft² and perimeter 12 ft.
Frequently asked questions
What is the Pythagorean theorem?
In any right triangle, a² + b² = c², where c is the hypotenuse. For legs 3 and 4, c = √(9 + 16) = 5.
How do I find a missing leg?
Choose “one leg and the hypotenuse” and enter them. The missing leg is √(c² − a²); for c = 13 and a = 5 it is 12.
What is the 3-4-5 rule in construction?
Measure 3 units along one line and 4 along the other; if the diagonal is exactly 5, the corner is square. Multiples like 6-8-10 work too.
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Sources
- Prealgebra 2e, 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem — OpenStax
- Precalculus 2e, 5.4 Right Triangle Trigonometry — OpenStax
- Right Triangle — Wolfram MathWorld
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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