Right Triangle Calculator

Right Triangle Calculator Calculate Right Triangle Properties Enter any two value...

Right Triangle Calculator

Calculate Right Triangle Properties

Enter any two values to calculate the rest:

Side a (leg)

Side b (leg)

Side c (hypotenuse)

Angle A (°)

Angle B (°)

💡 Pythagorean Theorem:
a² + b² = c²

💡 To save as PDF:
Click "Print or Save as PDF" above → Choose "Save as PDF" as your printer → Click "Save".

Triangle Properties

Side a (leg): 3.00

Side b (leg): 4.00

Side c (hypotenuse): 5.00

Angle A: 36.87°

Angle B: 53.13°

Angle C: 90.00°

Area: 6.00 square units

Perimeter: 12.00 units

Right Triangle Visualization

Key Formulas:

Pythagorean Theorem: a² + b² = c²

Area: A = ½ × a × b

Trigonometry: sin(A) = a/c, cos(A) = b/c, tan(A) = a/b

Perimeter: P = a + b + c

Understanding Right Triangles

Right triangles are fundamental geometric shapes with one 90-degree angle. They have special properties that make them essential in mathematics, engineering, architecture, and many real-world applications.

The Pythagorean Theorem (a² + b² = c²) is the cornerstone of right triangle calculations, relating the lengths of the two legs (a and b) to the hypotenuse (c). This theorem has been used for thousands of years in construction, navigation, and problem-solving.

Trigonometric ratios (sine, cosine, and tangent) are defined using right triangles and are crucial for solving problems involving angles and distances. These ratios form the basis of trigonometry and have applications in physics, engineering, computer graphics, and surveying.

This calculator helps students, teachers, and professionals quickly determine all properties of a right triangle when given any two values, making geometric calculations accessible and efficient.

Frequently Asked Questions

Q: What is the hypotenuse in a right triangle?
A: The hypotenuse is the longest side of a right triangle, opposite the 90-degree angle. It's always the side that the Pythagorean theorem solves for when you know the other two sides.

Q: How do I know which side is 'a' and which is 'b'?
A: In right triangle notation, sides 'a' and 'b' are the legs (the sides that form the right angle), and 'c' is always the hypotenuse. It doesn't matter which leg you call 'a' or 'b' - the calculations will work the same way.

Q: What are the most common right triangle ratios?
A: The most common right triangle ratios are 3-4-5, 5-12-13, 8-15-17, and 7-24-25. These are called Pythagorean triples because they satisfy the Pythagorean theorem with whole numbers. The 45-45-90 and 30-60-90 triangles are also very common special right triangles.

Q: Can I have negative side lengths?
A: No, side lengths in geometry are always positive. If you get a negative result in calculations, it usually indicates an error in your input values or that the triangle you're trying to create isn't possible.

Q: What is the relationship between the angles in a right triangle?
A: In any triangle, the angles sum to 180 degrees. In a right triangle, one angle is 90 degrees, so the other two angles must sum to 90 degrees. This means if you know one acute angle, you can find the other by subtracting from 90 degrees.

Q: How accurate are these calculations?
A: These calculations use JavaScript's built-in mathematical functions, which provide high precision (typically 15-17 decimal digits). For practical purposes in engineering, construction, and education, this level of accuracy is more than sufficient.

Q: What are some real-world applications of right triangles?
A: Right triangles are used in construction (ensuring square corners), navigation (GPS and triangulation), physics (vector resolution), computer graphics (3D rendering), surveying (distance measurement), and even in everyday tasks like hanging pictures or building furniture.