Updated Geometry & Trigonometry

Right Triangle Calculator

Solve right triangles step by step. Find missing sides, angles, area, perimeter and height, and check if three sides form a right triangle.

Sides & Angles Area & Perimeter Trig Ratios Pythagorean Check

All-in-One Right Triangle Calculator

Choose what you know the triangle and instantly find the rest of the sides and angles.

Right angle is at C. Side a is opposite angle A, side b is opposite angle B, and hypotenuse c is opposite the right angle.

Enter any acute angle of a right triangle (between 0° and 90°) to see its basic trigonometric ratios.

Order does not matter. The calculator detects the largest side as the possible hypotenuse and checks the Pythagorean theorem.

Right Triangle Calculator – How It Works

This Right Triangle Calculator uses the Pythagorean theorem and trigonometric functions to solve for missing sides and angles. You can solve the triangle from two sides, from a side and an angle, explore basic trig ratios, and check whether three lengths form a right triangle.

Right Triangle Basics

A right triangle has one angle equal to 90°. The sides are usually labeled so that the hypotenuse c is opposite the right angle, and the legs a and b form the right angle. The acute angles A and B always satisfy:

A + B = 90°

The Pythagorean theoremates the three sides:

c² = a² + b²

Solving a Right Triangle

If you know two pieces of information (such as two sides, or one side and one acute angle), you can solve the rest of the triangle. The calculator supports common combinations:

  • Two legs: a and b
  • One leg and the hypotenuse: a and c, or b and c
  • Hypotenuse and an acute angle: c and A, or c and B
  • Leg and its opposite acute angle: a and A, or b and B

From these inputs, it finds remaining sides using the Pythagorean theorem and angles using sine, cosine, and tangentationships.

Trig Ratios in a Right Triangle

For an acute angle θ in a right triangle, the basic trigonometric ratios are:

\[ \sin(θ) = \frac{\text{opposite}}{\text{hypotenuse}},\quad \cos(θ) = \frac{\text{adjacent}}{\text{hypotenuse}},\quad \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} \]

Their reciprocals are:

\[ \csc(θ) = \frac{1}{\sin(θ)},\quad \sec(θ) = \frac{1}{\cos(θ)},\quad \cot(θ) = \frac{1}{\tan(θ)} \]

Pythagorean Check

When you enter three side lengths, the Pythagorean Checker identifies the largest side as the potential hypotenuse and evaluates the expression:

c² − (a² + b²)

If this difference is zero (within rounding tolerance), the triangle is right-angled. A small non-zero difference indicates the sides are close to a Pythagorean triple but not exact.

Try more free tools on MyTimeCalculator for geometry, trigonometry, algebra, finance, health, and science to speed up your calculations and learning.

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