Calculate all properties (sides, angles, area, perimeter) of a right triangle.
The Right Triangle Calculator is a specialized geometric tool designed to solve all sides, angles, area, and perimeter of a right-angled triangle. A right triangle is a triangle with one interior angle of exactly 90 degrees. The side opposite this right angle is the hypotenuse (c), which is always the longest side, and the other two sides are the legs (a, b).
To solve a right triangle, you need to provide at least two known values, with at least one being a side length. The calculator utilizes the Pythagorean theorem (a² + b² = c²) and basic trigonometric ratios (Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent) to resolve the missing variables. For example, if angle A and side a are known, the hypotenuse is solved as c = a / sin(A), and side b as b = a / tan(A).
Right triangles are the basis of trigonometry, used to measure heights and distances that cannot be accessed directly, such as the height of trees or buildings (using clinometers). They are also used in physics to resolve vector forces into horizontal and vertical components. The right triangle calculator provides instant, precise geometric solutions, helping students, surveyors, and engineers layout structures and solve trigonometric equations.
Right Triangle Mathematics
A right triangle contains one 90° angle. Trigonometric properties:
- Angles: Angles A and B sum to 90°.
- Sine / Cosine / Tangent: Trigonometric ratios link the side lengths with the interior angles.
How it Works & Formula
Solves all angles, sides, perimeter, and area properties for a right-angled triangle.
Practical Examples
A ramp of height 3m and base 4m has slope length 5m and angle of inclination ≈ 36.87°.
Frequently Asked Questions
How are the acute angles determined?
Using inverse trigonometric functions: angle A = arctan(a/b) and angle B = 90° - angle A.