Right Triangle Calculator

Right Triangle Calculator

Enter any two values (sides or angles) and click “Calculate” to find the rest.

Right Triangle Calculator: Calculate Angles, Sides, Area, and More

Easily solve right triangle problems with our Right Triangle Calculator! Just enter two values to calculate the remaining angles, sides, area, and perimeter. Whether you’re working with degrees or radians, this tool can handle it all. You can even input values like π/3 or π/4 when selecting radians as the angle unit.

How to Use the Right Triangle Calculator

  1. Input any two known values (sides or angles).
  2. Select the angle unit (degrees or radians).
  3. Get instant calculations for:
  • Side lengths (a, b, c)
  • Angles (∠α, ∠β)
  • Hypotenuse (c)
  • Area (A)
  • Perimeter (P)
  • Altitude (h)

What Is a Right Triangle?

A right triangle is a type of triangle with one 90° angle. It is the foundation of trigonometry and is used in everything from geometry to real-world problem-solving. The side opposite the 90° angle is the longest side, called the hypotenuse (c), while the remaining two sides are referred to as a and b.

Key Features of a Right Triangle:

  • Hypotenuse (c): The longest side, opposite the 90° angle.
  • Angles (∠α, ∠β): The two other angles always add up to 90° in total.
  • Altitude (h): The perpendicular height from the 90° vertex to the hypotenuse.
  • Pythagorean Triangle: If all sides are integers, the triangle is a Pythagorean triangle (e.g., 3, 4, 5; 5, 12, 13).

How to Calculate the Area and Perimeter of a Right Triangle

  • Area (A): Use the formula A = 1/2 × a × b or A = 1/2 × c × h.
  • Perimeter (P): Add up the lengths of all three sides: P = a + b + c.

Special Right Triangles

30°-60°-90° Triangle:

A 30°-60°-90° triangle is a special right triangle with angles of 30°, 60°, and 90°. The sides follow a specific ratio: 1:√3:2.

  • If the side opposite the 60° angle is 5:
  • Side opposite 30°: a = 5/√3
  • Hypotenuse: c = 2 × (5/√3)

45°-45°-90° Triangle:

A 45°-45°-90° triangle, also called an isosceles right triangle, has two equal angles (45° each) and follows the ratio 1:1:√2.

  • If the hypotenuse is 5:
  • Each leg: a = 5/√2

These special triangles are useful for evaluating trigonometric functions like sine, cosine, and tangent for common angles.

Explore the Basics of Right Triangles

Right triangles are essential in mathematics, especially in geometry and trigonometry. They can also be used to solve real-world problems like calculating heights, distances, or slopes. Whether you’re working with the Pythagorean theorem or exploring special right triangles, understanding their properties is key.

Related Tools

Optimize your calculations today with our easy-to-use Right Triangle Calculator! Designed to help students, engineers, and math enthusiasts, it’s your go-to tool for solving triangle problems efficiently.