Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8.49   b = 3.16   c = 5.83

Area: T = 5.95664748803
Perimeter: p = 17.48
Semiperimeter: s = 8.74

Angle ∠ A = α = 139.7111127494° = 139°42'40″ = 2.43884191764 rad
Angle ∠ B = β = 13.92767781627° = 13°55'36″ = 0.24330681331 rad
Angle ∠ C = γ = 26.36220943437° = 26°21'44″ = 0.4660105344 rad

Height: ha = 1.40331742945
Height: hb = 3.77699208103
Height: hc = 2.0433387609

Median: ma = 1.99217893965
Median: mb = 7.1099015403
Median: mc = 5.70440007889

Inradius: r = 0.6821518865
Circumradius: R = 6.56546869643

Vertex coordinates: A[5.83; 0] B[0; 0] C[8.24404288165; 2.0433387609]
Centroid: CG[4.69901429388; 0.6811129203]
Coordinates of the circumscribed circle: U[2.915; 5.88219971046]
Coordinates of the inscribed circle: I[5.58; 0.6821518865]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 40.28988725063° = 40°17'20″ = 2.43884191764 rad
∠ B' = β' = 166.0733221837° = 166°4'24″ = 0.24330681331 rad
∠ C' = γ' = 153.6387905656° = 153°38'16″ = 0.4660105344 rad

Calculate another triangle


How did we calculate this triangle?

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

p = a+b+c = 8.49+3.16+5.83 = 17.48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.48 }{ 2 } = 8.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.74 * (8.74-8.49)(8.74-3.16)(8.74-5.83) } ; ; T = sqrt{ 35.48 } = 5.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.96 }{ 8.49 } = 1.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.96 }{ 3.16 } = 3.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.96 }{ 5.83 } = 2.04 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 3.16**2+5.83**2-8.49**2 }{ 2 * 3.16 * 5.83 } ) = 139° 42'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.49**2+5.83**2-3.16**2 }{ 2 * 8.49 * 5.83 } ) = 13° 55'36" ; ; gamma = 180° - alpha - beta = 180° - 139° 42'40" - 13° 55'36" = 26° 21'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.96 }{ 8.74 } = 0.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.49 }{ 2 * sin 139° 42'40" } = 6.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 5.83**2 - 8.49**2 } }{ 2 } = 1.992 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.83**2+2 * 8.49**2 - 3.16**2 } }{ 2 } = 7.109 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 8.49**2 - 5.83**2 } }{ 2 } = 5.704 ; ;
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.