Base (leg a)
3.000
Units
Height (leg b)
4.000
Units
Hypotenuse
5.000
Units
Area
6.000
Square units
Perimeter
12.000
Units around the triangle
Aspect Ratio
1.333
Height ÷ Base
Altitude & radii
- Altitude to hypotenuse
- 2.400
- Inscribed circle radius
- 1.000
- Circumcircle radius
- 2.500
Proportions
- Leg ratio (b ÷ a)
- 1.333
- Leg difference
- 1.000
- Complementary angles
- 53.13° / 36.87°
Scaled triangle diagram
Diagram scaled by longest leg for visual comparison.
Angle + trig breakdown
| Angle | Measure (°) | Sine | Cosine | Tangent |
|---|---|---|---|---|
| ∠A (base ↔ hypotenuse) | 53.130 | 0.8000 | 0.6000 | 1.3333 |
| ∠B (height ↔ hypotenuse) | 36.870 | 0.6000 | 0.8000 | 0.7500 |
| ∠C (right angle) | 90.000 | 1.0000 | 0.0000 | — |
Geometry insights
-
Scalene right triangle
All three sides differ in length, leading to complementary acute angles.
-
Pythagorean triple detected
Side lengths closely match the 3-4-5 integer triple.
-
Shape proportion
The triangle is taller than it is wide with an aspect ratio of about 1.33:1.
-
Inradius and altitude
The inscribed circle radius is 1.000 and the altitude to the hypotenuse is 2.400.
Quick reference
- Area is always half of base × height for a right triangle.
- Use sine and cosine to project any other lengths from the hypotenuse.
- Complementary acute angles always sum to 90°. Knowing one angle automatically gives the other.
Solve any right triangle instantly with our comprehensive calculator that finds missing sides, angles, area, perimeter, and advanced geometric properties. Perfect for students, engineers, architects, and anyone working with trigonometry and geometry calculations.
Advanced Features:
- Complete Triangle Analysis: Calculate all sides, angles, area, perimeter, and altitude from any two known values
- Visual Diagram: Scaled triangle representation with proportional accuracy and angle markings
- Trigonometry Table: Complete sine, cosine, and tangent values for all angles
- Pythagorean Triple Detection: Automatically identifies integer triangle relationships
- Geometry Insights: Provides aspect ratios, complementary angles, and shape analysis
- Circle Properties: Calculates inscribed and circumscribed circle radii
Perfect for:
- Students learning geometry, trigonometry, and the Pythagorean theorem
- Engineers & Architects requiring precise triangle calculations for structural design
- Educators teaching geometric concepts with visual demonstrations
- Professionals in construction, surveying, and technical fields
How It Works: Simply input any two known values (sides or angles) and our right triangle solver instantly calculates all remaining properties. The tool handles various input combinations including base and height, hypotenuse and angle, or any side-angle pairs.
Mathematical Foundation: Built on fundamental geometric principles including the Pythagorean theorem (a² + b² = c²), trigonometric ratios (sine, cosine, tangent), and triangle area formulas. Our calculator ensures accuracy for academic work, professional projects, and real-world applications.
Unique Benefits:
- Instant Results: No complex formulas to remember
- Visual Learning: Scaled diagrams enhance understanding
- Complete Solutions: More than basic calculators - includes advanced properties
- Educational Value: Geometry insights explain triangle relationships
Start solving your right triangle problems today with our free, comprehensive calculator tool.
API Documentation Coming Soon
Documentation for this tool is being prepared. Please check back later or visit our full API documentation.
