What is a Right Triangle?

A right triangle, or right-angled triangle, is a fundamental polygon in Euclidean geometry characterized by one internal angle measuring exactly 90 degrees. This angle is known as the right angle. The side opposite this right angle is always the longest side, referred to as the hypotenuse. The other two sides are known as the legs or catheti.

The Pythagorean Theorem

The relationship between the sides of a right triangle is defined by the famous Pythagorean theorem: a² + b² = c². This mathematical principle states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Our right triangle calculator online uses this theorem to solve for missing side lengths automatically.

How to Use This Calculator

To solve a right triangle using this tool, you must provide at least two known values, one of which must be a side length. Follow these steps:

• Input Sides: If you know two sides (e.g., A and B), enter them to find the hypotenuse and both acute angles.
• Input Side & Angle: If you know one side and one angle (other than the 90° angle), enter them to solve for all remaining dimensions.
• Accuracy: All calculations are performed using high-precision trigonometric functions (Sine, Cosine, Tangent).

Frequently Asked Questions

Can a right triangle have two 90-degree angles?

No. In Euclidean geometry, the sum of all angles in a triangle must equal 180 degrees. If a triangle had two 90-degree angles, the third angle would have to be 0 degrees, which is impossible for a triangle.

What are SOH CAH TOA?

These are mnemonics used to remember trigonometric ratios: Sine = Opposite/Hypotenuse (SOH), Cosine = Adjacent/Hypotenuse (CAH), and Tangent = Opposite/Adjacent (TOA). These ratios are the engine behind our right triangle calculator's angle logic.

What is the Area of a Right Triangle?

The area of a right triangle is calculated by multiplying the two legs (base and height) and dividing by two: Area = (a × b) / 2.