Right Triangle Calculator
Calculate all properties of right triangles from any two known values. Find sides, angles, area, trigonometric ratios, and verify triangle validity with step-by-step solutions.
Right Triangle Calculator
Input Values
Calculate hypotenuse and angles from two perpendicular sides using Pythagorean theorem.
Results
Sides
Side a (opposite to ∠A):3.000 cm
Side b (opposite to ∠B):4.000 cm
Hypotenuse c:5.000 cm
Angles
Angle A:36.870°
Angle B:53.130°
Angle C (right angle):90.000°
Area
6.000 cm²
A = ½ab
Perimeter
12.000 cm
P = a + b + c
Altitude to Hypotenuse
2.400 cm
h = ab/c
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What is Right Triangle Calculator?
A right triangle calculator helps you find all properties of right triangles (triangles with one 90° angle) using various combinations of known values. Right triangles are fundamental in mathematics, physics, engineering, and many practical applications.
Calculation Methods
- Two Sides:Given two perpendicular sides (a and b), calculate hypotenuse using Pythagorean theorem
- Hypotenuse & Side:Given hypotenuse and one side, find the other side and all angles
- Side & Angle:Given one side and one acute angle, calculate all other properties
- Hypotenuse & Angle:Given hypotenuse and one acute angle, find both sides
- Verify Triangle:Check if three given sides actually form a right triangle
Right Triangle Properties
- Sides:Two legs (a and b) and hypotenuse (c, the longest side opposite the right angle)
- Angles:One right angle (90°) and two complementary acute angles (sum to 90°)
- Area:½ × base × height = ½ab (using the two legs)
- Perimeter:Sum of all three sides (a + b + c)
- Altitude to Hypotenuse:Height from right angle to hypotenuse (h = ab/c)
Special Right Triangles
- 45-45-90 Triangle:Isosceles right triangle with legs equal, hypotenuse = leg × √2
- 30-60-90 Triangle:Half of an equilateral triangle with sides in ratio 1 : √3 : 2
- 3-4-5 Triangle:Classic Pythagorean triple, commonly used in construction
- 5-12-13 Triangle:Another Pythagorean triple useful for larger measurements
Trigonometric Functions
- Sine (sin):opposite side ÷ hypotenuse
- Cosine (cos):adjacent side ÷ hypotenuse
- Tangent (tan):opposite side ÷ adjacent side
- Complementary Relationships:sin A = cos B, cos A = sin B (for acute angles A and B)
Key Formulas
- Pythagorean Theorem:a² + b² = c²
- Area:A = ½ab (using legs as base and height)
- Trigonometric Relations:sin² θ + cos² θ = 1
- Angle Sum:A + B = 90° (for acute angles in right triangle)
Practical Applications
- Construction:Ensuring square corners, calculating diagonal braces
- Navigation:Distance and bearing calculations
- Architecture:Roof pitch, ramp slopes, structural design
- Surveying:Land measurement and triangulation
- Physics:Vector components, force analysis
FAQ - Right Triangle Calculator
A right triangle has exactly one angle that measures 90° (a right angle). This creates special relationships between the sides that follow the Pythagorean theorem: the square of the hypotenuse equals the sum of squares of the other two sides (a² + b² = c²).