Right Triangle Calculator
Solve using Pythagorean theorem and trigonometry
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Right Triangle Diagram
About Right Triangles
A right triangle is a triangle with one 90-degree angle. The side opposite the right angle is called the hypotenuse, and it's always the longest side. The other two sides are called legs.
Pythagorean Theorem
The fundamental relationship in right triangles: a² + b² = c²
Where a and b are the legs, and c is the hypotenuse.
Trigonometric Ratios
- Sine: sin(A) = opposite/hypotenuse = a/c
- Cosine: cos(A) = adjacent/hypotenuse = b/c
- Tangent: tan(A) = opposite/adjacent = a/b
Special Right Triangles
- 45-45-90 Triangle: Sides in ratio 1:1:√2
- 30-60-90 Triangle: Sides in ratio 1:√3:2
Frequently Asked Questions
What is a right triangle?
A right triangle has one angle that measures exactly 90 degrees. The other two angles are acute (less than 90°) and together sum to 90°.
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c².
Which side is the hypotenuse?
The hypotenuse is the side opposite the right angle, and it's always the longest side of a right triangle.
How do I use SOH CAH TOA?
SOH CAH TOA is a mnemonic for remembering trig ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
Can I solve with just one side and one angle?
Yes, if you know one acute angle, you automatically know the other (90° - given angle). Then use trig ratios with the known side to find the others.
What are Pythagorean triples?
Pythagorean triples are sets of three integers that satisfy a² + b² = c². Common examples: (3,4,5), (5,12,13), (8,15,17).
How do I find the area of a right triangle?
Area = ½ × base × height. For a right triangle, the two legs are the base and height, so Area = ½ × a × b.
Why do the acute angles sum to 90°?
Since all triangle angles sum to 180°, and one angle is 90°, the other two must sum to 180° - 90° = 90°.