About the right triangle calculator
The right triangle calculator solves a right triangle from any two suitable known values: legs, hypotenuse, an acute angle, the area, the perimeter or the altitude to the hypotenuse. It returns the two legs, the hypotenuse, both acute angles, area, perimeter, altitude, inradius and circumradius, and draws the triangle.
Who should use the right triangle calculator
- Trigonometry students.
- Builders, designers and surveyors working with slopes and heights.
- Anyone who knows two measurements and needs the rest.
How to use the right triangle calculator: what each input means
- First and second known value
- Choose which measurements you know and enter their values. The two must be different kinds.
How the right triangle calculator works: method and formula
The right angle is at C, leg a is opposite angle α, leg b is opposite angle β and c is the hypotenuse. The calculator uses the Pythagorean theorem and the trigonometric ratios (sine, cosine, tangent) to find the missing parts. Combinations that involve area, perimeter or altitude are solved algebraically.
- Pythagoras
- a² + b² = c²
- Ratios
- sin α = a ÷ c, cos α = b ÷ c, tan α = a ÷ b
- Area and altitude
- Area = ½ab, h = ab ÷ c
How to read your right triangle calculator result
The two acute angles always add to 90°. If your inputs cannot describe a real right triangle, for example a leg longer than the hypotenuse, the calculator explains the problem.
Right Triangle Calculator worked example
Legs a = 3 and b = 4.
- c = √(3² + 4²) = 5.
- α = arctan(3 ÷ 4) = 36.870° and β = 53.130°.
- Area = ½ × 3 × 4 = 6; perimeter = 12; altitude to the hypotenuse = 2.4.
Hypotenuse 5, angles 36.87° and 53.13°.
Practical uses of the right triangle calculator
- Working out a ramp's length and angle.
- Finding the height of an object from distance and angle of elevation.
- Checking trigonometry exercises.
Assumptions and limitations of this calculator
- Flat right triangles only.
- Some combinations of two values do not determine a unique triangle or cannot exist; the calculator reports this.
- Angles are in degrees.