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Triangle Calculator

Solve right triangles instantly. Find area, hypotenuse, and interior angles.

Right Triangle Calculator

Enter the base and height of a right triangle to solve for area, hypotenuse, perimeter, and angles.

Understanding Right Triangle Mathematics

A right triangle is one of the most fundamental shapes in geometry, characterized by having one angle that measures exactly 90 degrees. This unique property makes it the cornerstone of trigonometry, architecture, navigation, and surveying. The Calculay Triangle Calculator helps you solve for all unknown dimensions (Area, Perimeter, Hypotenuse, and Angles) instantly by just providing the two legs (Base and Height).

The Pythagorean Theorem

Discovered in ancient Greece, the Pythagorean Theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides:

a2 + b2 = c2

By knowing the Base (a) and the Height (b), our calculator can effortlessly determine the length of the Hypotenuse (c).

How is the Area Calculated?

The area of a right triangle is exactly half of the area of the rectangle formed by its base and height.

  • Area Formula: Area = ½ × Base × Height

Trigonometric Angles

Beyond simple side lengths, a right triangle has two unknown acute angles (which always sum to exactly 90 degrees). By using Inverse Trigonometric functions (SOH CAH TOA), the calculator will determine the precise interior angles in degrees.

  • Angle A: Calculated using the arc-tangent of (Height / Base).
  • Angle B: Calculated by subtracting Angle A from 90°.
Real World Use Case: If you are building a wheelchair ramp, a staircase, or cutting lumber for a pitched roof, you are dealing with right triangles. Simply enter the horizontal run (Base) and the vertical rise (Height) to find exactly how long the ramp or rafter (Hypotenuse) needs to be, and at what angle it needs to be cut.