Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 1.85   b = 1.85   c = 1.9

Area: T = 1.50880782473
Perimeter: p = 5.6
Semiperimeter: s = 2.8

Angle ∠ A = α = 59.10218521748° = 59°6'7″ = 1.03215219145 rad
Angle ∠ B = β = 59.10218521748° = 59°6'7″ = 1.03215219145 rad
Angle ∠ C = γ = 61.79662956505° = 61°47'47″ = 1.07985488246 rad

Height: ha = 1.6330354862
Height: hb = 1.6330354862
Height: hc = 1.58774507866

Median: ma = 1.63111422378
Median: mb = 1.63111422378
Median: mc = 1.58774507866

Inradius: r = 0.5398599374
Circumradius: R = 1.07879861741

Vertex coordinates: A[1.9; 0] B[0; 0] C[0.95; 1.58774507866]
Centroid: CG[0.95; 0.52991502622]
Coordinates of the circumscribed circle: U[0.95; 0.50994646126]
Coordinates of the inscribed circle: I[0.95; 0.5398599374]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.8988147825° = 120°53'53″ = 1.03215219145 rad
∠ B' = β' = 120.8988147825° = 120°53'53″ = 1.03215219145 rad
∠ C' = γ' = 118.204370435° = 118°12'13″ = 1.07985488246 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 1.85 ; ; b = 1.85 ; ; c = 1.9 ; ;

2. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 1.85+1.85+1.9 = 5.6 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.6 }{ 2 } = 2.8 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.8 * (2.8-1.85)(2.8-1.85)(2.8-1.9) } ; ; T = sqrt{ 2.27 } = 1.51 ; ;

5. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.51 }{ 1.85 } = 1.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.51 }{ 1.85 } = 1.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.51 }{ 1.9 } = 1.59 ; ;

6. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 1.85**2+1.9**2-1.85**2 }{ 2 * 1.85 * 1.9 } ) = 59° 6'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.85**2+1.9**2-1.85**2 }{ 2 * 1.85 * 1.9 } ) = 59° 6'7" ; ; gamma = 180° - alpha - beta = 180° - 59° 6'7" - 59° 6'7" = 61° 47'47" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.51 }{ 2.8 } = 0.54 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.85 }{ 2 * sin 59° 6'7" } = 1.08 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.85**2+2 * 1.9**2 - 1.85**2 } }{ 2 } = 1.631 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.9**2+2 * 1.85**2 - 1.85**2 } }{ 2 } = 1.631 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.85**2+2 * 1.85**2 - 1.9**2 } }{ 2 } = 1.587 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.