Right Triangle Side and Angle Calculator: Complete Guide (2026)
Calculate all sides and angles of a right triangle from any two values. Find hypotenuse, legs, angles, area, and perimeter with step-by-step trig solutions.
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Put these formulas into practice with our instant, step-by-step Right Triangle Side and Angle Calculator.
The right triangle is the most important triangle in mathematics, forming the foundation of trigonometry and appearing in countless applications from navigation to physics. A right triangle has one angle of exactly 90 degrees, and the side opposite this angle is called the hypotenuse. Our free right triangle calculator solves for all properties from any two known values.
Key Takeaway
A right triangle calculator uses the Pythagorean theorem (a² + b² = c²) and trigonometric ratios (sin, cos, tan) to solve for all sides and angles from any two known values.
What is a Right Triangle?
A right triangle (or right-angled triangle) is a triangle with one angle of exactly 90 degrees. The side opposite the right angle is called the hypotenuse (the longest side), and the other two sides are called legs.
Fundamental Formulas
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
Area = (a × b) / 2
How to Use the Right Triangle Calculator
- Enter any two known values (two sides, a side and angle, etc.)
- The calculator automatically solves for all remaining values
- View the complete triangle solution with area and perimeter
- Copy the results to your clipboard
Worked Example
Hypotenuse = 13, One Leg = 5
| Property | Calculation | Result |
|---|---|---|
| Other leg | √(13² - 5²) | 12 |
| Angle A | arcsin(5/13) | 22.62° |
| Angle B | 90° - 22.62° | 67.38° |
| Area | (5 × 12) / 2 | 30 |
| Perimeter | 5 + 12 + 13 | 30 |
Real-World Applications
- Navigation: GPS, bearings, and distance calculations
- Physics: Vector decomposition and force analysis
- Construction: Roof pitches, ramp angles, and structural supports
- Astronomy: Parallax measurements and stellar distances
- Computer Graphics: 3D rendering and collision detection
Frequently Asked Questions
How do I find the hypotenuse from two legs?
Use the Pythagorean theorem: c = √(a² + b²). For legs 3 and 4: c = √(9 + 16) = √25 = 5.
What is SOH-CAH-TOA?
SOH: sin(θ) = Opposite/Hypotenuse. CAH: cos(θ) = Adjacent/Hypotenuse. TOA: tan(θ) = Opposite/Adjacent. This mnemonic helps remember which trigonometric ratio to use.
Try our right triangle calculator to solve any right triangle instantly, or explore our Pythagorean triples calculator and similar triangles calculator for more triangle computations.