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How It Works
Select a triangle type and enter the known measurements. For right triangles the calculator uses the Pythagorean theorem. For equilateral triangles it applies s-based formulas. The law of cosines and law of sines handle oblique triangles where you know two sides and an included angle, or a side-angle pair.
Example Problem
A right triangle has legs 3 and 4. Find the hypotenuse, area, and perimeter:
- Hypotenuse = √(3² + 4²) = √25 = 5
- Area = ½ × 3 × 4 = 6
- Perimeter = 3 + 4 + 5 = 12
Frequently Asked Questions
How to find the hypotenuse of a right triangle?
Use the Pythagorean theorem c = √(a² + b²). For legs of 5 and 12, the hypotenuse is √(25 + 144) = √169 = 13.
When do you use the law of cosines vs. the law of sines?
Use the law of cosines when you know two sides and the included angle (SAS), or all three sides (SSS). Use the law of sines when you know a side and its opposite angle plus one more measurement (AAS or ASA).
What is the area formula for an equilateral triangle?
A = (√3/4)s². For a side length of 6, the area is (√3/4) × 36 = 9√3 ≈ 15.59 square units. The altitude is (√3/2) × 6 ≈ 5.20.
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