Right Triangles Calculator

  • Enter side lengths and angles for your right triangle.
  • Click "Calculate" to calculate the results.
  • The calculation details, including formulas used, will be displayed.
  • A bar chart will visually represent the side lengths and angles.
  • Your calculation history will be displayed below.
  • Click "Clear" to reset the inputs and calculation details.
  • Click "Copy Results" to copy the calculation details to the clipboard.
Calculation History:

    What is Right Triangle?

    A right triangle is a type of triangle that has one of its angles measuring exactly 90 degrees (a right angle). This specific angle is denoted by a square symbol (∟) in diagrams. Right triangles are fundamental geometric shapes and have several unique properties.

    All Formulae Related to Right Triangles

    Here are some important formulae and relationships related to right triangles:

    1. Pythagorean Theorem:
      • c² = a² + b²
      • Where “c” represents the length of the hypotenuse, and “a” and “b” represent the lengths of the other two sides.
    2. Trigonometric Functions:
      • Sine (sin) of an angle θ:
        • sin(θ) = Opposite side / Hypotenuse
        • sin(θ) = a / c
      • Cosine (cos) of an angle θ:
        • cos(θ) = Adjacent side / Hypotenuse
        • cos(θ) = b / c
      • Tangent (tan) of an angle θ:
        • tan(θ) = Opposite side / Adjacent side
        • tan(θ) = a / b
    3. Reciprocal Trigonometric Functions:
      • Cosecant (csc) of an angle θ:
        • csc(θ) = 1 / sin(θ)
        • csc(θ) = c / a
      • Secant (sec) of an angle θ:
        • sec(θ) = 1 / cos(θ)
        • sec(θ) = c / b
      • Cotangent (cot) of an angle θ:
        • cot(θ) = 1 / tan(θ)
        • cot(θ) = b / a
    4. Special Right Triangles:
      • For a 45-45-90 triangle with legs of length “x”:
        • Hypotenuse = x√2
      • For a 30-60-90 triangle with shorter leg of length “x”:
        • Longer leg = x√3
        • Hypotenuse = 2x
    5. Area of a Right Triangle:
      • Area = (1/2) * base * height
      • Area = (1/2) * a * b

    Practical Uses of Right Triangles Calculator

    A right triangle calculator is a useful tool for solving various practical problems that involve right triangles. Here are some practical uses of a right triangle calculator:

    1. Geometry and Construction:
      • Calculate the length of a missing side (either a leg or the hypotenuse) when the lengths of the other two sides are known.
      • Determine the angles of a right triangle when the lengths of the sides are given.
      • Find the area of a right triangle when the lengths of its base and height are provided.
      • Verify if a triangle is a right triangle by checking if the Pythagorean theorem holds true.
    2. Trigonometry:
      • Solve trigonometric problems involving right triangles, such as finding the value of sine, cosine, or tangent of an angle when the lengths of sides are given.
      • Determine unknown angles in right triangles using inverse trigonometric functions.
    3. Physics:
      • Calculate the displacement or velocity of an object moving along a ramp or inclined plane.
      • Determine the forces acting on an object on an inclined plane.
    4. Engineering and Architecture:
      • Design and analyze structures that involve right angles and right triangles, such as roofs, ramps, and supports.
      • Calculate distances and heights in construction projects, surveying, and land measurement.
    5. Navigation:
      • Determine distances or heights when using triangulation or trigonometric methods for navigation and map reading.
      • Calculate elevation changes and slopes when navigating in hilly or mountainous terrain.
    6. Electronics:
      • Calculate the impedance or phase angle in electrical circuits that involve right triangles, such as those in AC circuits.

    Applications of Right Triangles in Various Fields

    Right triangles have a wide range of applications in various fields due to their simplicity and the fundamental trigonometric relationships they exhibit. Here are some practical applications of right triangles in different fields:

    1. Architecture and Construction:
      • Architects use right triangles to ensure structural stability and design buildings with proper angles and dimensions.
      • Construction workers rely on right triangles to create square corners and measure distances on construction sites accurately.
    2. Engineering:
      • Civil engineers use right triangles to calculate slopes, angles, and distances when designing roads, bridges, and other infrastructure.
      • Mechanical engineers use trigonometry to analyze mechanical systems involving angles and forces.
    3. Physics:
      • Right triangles are used to analyze forces, motion, and energy in physics problems.
      • In kinematics, right triangles help calculate the components of velocity or acceleration in different directions.
    4. Astronomy:
      • Astronomers use right triangles for celestial navigation and determining the positions and distances of celestial objects.
      • Parallax measurements involve the use of right triangles to determine the distances to stars.
    5. Navigation:
      • Navigators and pilots use right triangles for dead reckoning and celestial navigation to determine positions, distances, and headings.
      • GPS systems rely on the principles of trilateration, which involve right triangles, to determine precise locations.


    1. “Right Triangles in Number Theory” by Kenneth H. Rosen
    2. “Right Triangles in Fractal Geometry” by Benoit B. Mandelbrot

    Last Updated : 27 February, 2024

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