Right Triangle Calculator | Solve Sides, Angles & Area
Solve sides, angles, area, perimeter, altitude, inradius, and circumradius of any right-angled triangle. Enter any two variables to get step-by-step...
* Note: Entering only angles (α and β) is mathematically insufficient to scale the triangle. At least one side length must be provided.
Trigonometric Slider Explorer
Drag the slider to adjust angle α and hypotenuse to observe how sides scale dynamically.
Angle α: 30°Angle β: 60°
Hypotenuse c: 10
Solving Case Category
Valid Right TriangleSolved via Leg a & Leg b
Leg a
3
Leg b
4
Hypotenuse c
5
Angle α
36.869898° (0.6435 rad)
Angle β
53.130102° (0.9273 rad)
Right Angle γ
90.00° (1.5708 rad)
Proportionally Scaled Diagram
Geometric & Secondary Metrics
Perimeter (P)
12 units
Formula: a + b + c
Area (A)
6 sq units
Formula: 0.5 * a * b
Altitude to Hypotenuse (h_c)
2.4 units
Formula: (a * b) / c
Inradius (r_in)
1 units
Formula: (a + b - c) / 2
Circumradius (R_circum)
2.5 units
Formula: c / 2 (Center of circumcircle is always hypotenuse midpoint)
Step-by-Step Mathematical Solver
1. Solve Hypotenuse (c) using Pythagorean Theorem:
c = √(a² + b²) = √(3² + 4²)
c = √(9.00 + 16.00) = √(25.00) = 5
2. Solve Angle α using Tangent (tan) ratio:
tan(α) = a / b = 3 / 4 = 0.7500
α = arctan(0.7500) ≈ 36.869898°
3. Solve Angle β (complementary):
β = 90° - α = 90° - 36.869898° = 53.130102°
3. Secondary Attributes:
Perimeter = a + b + c = 3 + 4 + 5 = 12
Area = 0.5 * a * b = 0.5 * 3 * 4 = 6
Altitude to Hypotenuse = (a * b) / c = (3 * 4) / 5 = 2.4