Right Triangle Calculator

Calculate all properties of right triangles including sides, angles, area, and perimeter. Essential for mathematics, engineering, and construction.

How to Use Right Triangle Calculator

1. 1.**Enter any two values**: two sides or one side and hypotenuse
2. 2.**Click "Calculate Triangle"** to find all properties
3. 3.**View complete results** for all triangle measurements
4. 4.**Check angles and area** automatically calculated

Features

• •**Multiple Inputs**: Use any two known values
• •**Complete Results**: All triangle properties calculated
• •**Angle Calculation**: Automatic angle determination
• •**Area & Perimeter**: Additional properties included

Right Triangle Formulas

Pythagorean Theorem

a² + b² = c²

Trigonometric Functions

• •**sin(A) = a/c**
• •**cos(A) = b/c**
• •**tan(A) = a/b**

Area

A = ½ × a × b

Perimeter

P = a + b + c

Common Applications

• •**Construction**: Roof pitch, stairs, ramps
• •**Engineering**: Force vectors, structural analysis
• •**Surveying**: Land measurement, elevation
• •**Navigation**: Triangulation, positioning
• •**Design**: Layout planning, space allocation

Triangle Properties

• •**Right Angle**: Always 90° at the intersection of sides a and b
• •**Angles**: A + B = 90° (complementary angles)
• •**Hypotenuse**: Always opposite the right angle
• •**Legs**: The two sides forming the right angle

Practical Examples

• •**3-4-5 Triangle**: Sides 3, 4, hypotenuse 5, angles 36.9°, 53.1°
• •**TV Screen**: 24" × 18" = 30" diagonal, angles 36.9°, 53.1°
• •**Roof Pitch**: 8ft rise, 12ft run = 14.4ft rafter
• •**Ladder**: 10ft ladder, 6ft from wall = 8ft reach

Tips for Using Right Triangle Calculator

• •**Enter any two values** to calculate all properties
• •**Use consistent units** for all measurements
• •**Verify right angle** (90°) in real applications
• •**Consider precision** for engineering applications
• •**Check triangle validity** before using results

Special Right Triangles

• •**45-45-90**: Isosceles right triangle
• •**30-60-90**: Half of equilateral triangle
• •**3-4-5**: Common Pythagorean triple
• •**5-12-13**: Another common triple

Angle Relationships

• •**Angle A + Angle B = 90°** (complementary)
• •**sin²(A) + cos²(A) = 1** (Pythagorean identity)
• •**tan(A) = sin(A)/cos(A)** (tangent ratio)
• •**Angles determine side ratios** uniquely