Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 1.73   b = 1.41   c = 0.52

Area: T = 0.31773115189
Perimeter: p = 3.66
Semiperimeter: s = 1.83

Angle ∠ A = α = 120.0544155101° = 120°3'15″ = 2.09553402872 rad
Angle ∠ B = β = 44.86659299052° = 44°51'57″ = 0.78330581988 rad
Angle ∠ C = γ = 15.08799149934° = 15°4'48″ = 0.26331941676 rad

Height: ha = 0.36768341258
Height: hb = 0.45500872608
Height: hc = 1.22204289187

Median: ma = 0.61772722252
Median: mb = 1.06551877769
Median: mc = 1.55765667348

Inradius: r = 0.17333942726
Circumradius: R = 0.99993617664

Vertex coordinates: A[0.52; 0] B[0; 0] C[1.22661538462; 1.22204289187]
Centroid: CG[0.58220512821; 0.40768096396]
Coordinates of the circumscribed circle: U[0.26; 0.9654947636]
Coordinates of the inscribed circle: I[0.42; 0.17333942726]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 59.94658448986° = 59°56'45″ = 2.09553402872 rad
∠ B' = β' = 135.1344070095° = 135°8'3″ = 0.78330581988 rad
∠ C' = γ' = 164.9220085007° = 164°55'12″ = 0.26331941676 rad

Calculate another triangle




How did we calculate this triangle?

a = 1.73 ; ; b = 1.41 ; ; c = 0.52 ; ;

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

p = a+b+c = 1.73+1.41+0.52 = 3.66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.66 }{ 2 } = 1.83 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.83 * (1.83-1.73)(1.83-1.41)(1.83-0.52) } ; ; T = sqrt{ 0.1 } = 0.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.32 }{ 1.73 } = 0.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.32 }{ 1.41 } = 0.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.32 }{ 0.52 } = 1.22 ; ;

5. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 1.73**2-1.41**2-0.52**2 }{ 2 * 1.41 * 0.52 } ) = 120° 3'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.41**2-1.73**2-0.52**2 }{ 2 * 1.73 * 0.52 } ) = 44° 51'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.52**2-1.73**2-1.41**2 }{ 2 * 1.41 * 1.73 } ) = 15° 4'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.32 }{ 1.83 } = 0.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.73 }{ 2 * sin 120° 3'15" } = 1 ; ;

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

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