Geometry

Right Triangle Calculator: Calculate Sides and Angles

Calculate sides, angles, and trigonometric functions of right triangles easily with our online calculator. Ideal for students and professionals.

Right Triangle Calculator

Enter two known values to calculate the remaining sides and angles of a right triangle.

Right Triangle

Right Triangle Results:

Side a:
Side b:
Hypotenuse c:
Angle A: °
Angle B: °
Angle C: 90° (Right Angle)

Trigonometric Functions Calculator

Calculate sine, cosine, tangent, cosecant, secant, and cotangent for a given angle.

Trigonometric Function Results:

sin(°):
cos(°):
tan(°):
cosec(°):
sec(°):
cot(°):

Understanding Right Triangles & Trigonometry

A right triangle is defined by having one angle that measures exactly 90 degrees. The longest side, opposite the right angle, is known as the hypotenuse (c). The other two sides are called legs (a and b).

Key Concepts

  • Pythagorean Theorem: In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Formula: a2 + b2 = c2.
  • Angles: The sum of angles in any triangle is 180°. In a right triangle, one angle is 90°, so the other two acute angles sum to 90°.
  • Trigonometric Functions: These functions relate the angles of a right triangle to the ratios of its sides. The primary functions are:
    • Sine (sin): Ratio of the length of the opposite side to the hypotenuse. sin(θ) = Opposite / Hypotenuse
    • Cosine (cos): Ratio of the length of the adjacent side to the hypotenuse. cos(θ) = Adjacent / Hypotenuse
    • Tangent (tan): Ratio of the length of the opposite side to the adjacent side. tan(θ) = Opposite / Adjacent
  • Reciprocal Trigonometric Functions:
    • Cosecant (cosec): cosec(θ) = 1 / sin(θ)
    • Secant (sec): sec(θ) = 1 / cos(θ)
    • Cotangent (cot): cot(θ) = 1 / tan(θ)

How to Use This Calculator

Simply input two known values of your right triangle - these can be two side lengths, or one side length and one acute angle. The calculator will then determine the remaining sides and angles. For trigonometric functions, enter any angle in degrees to calculate the values of sin, cos, tan, cosec, sec, and cot for that angle. Use the 'Reset' button to clear inputs and start afresh.

Frequently Asked Questions

What is the Right Triangle Calculator: Calculate Sides and Angles?
The Right Triangle Calculator: Calculate Sides and Angles is an online Geometry calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Right Triangle Calculator: Calculate Sides and Angles?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Right Triangle Calculator: Calculate Sides and Angles for professional Geometry projects?
Yes. The math behind it is standard Geometry, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Right Triangle Calculator: Calculate Sides and Angles instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Right Triangle Calculator: Calculate Sides and Angles?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.

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