Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8   b = 19   c = 26

Area: T = 42.87770043263
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 9.99766798764° = 9°59'48″ = 0.17444749781 rad
Angle ∠ B = β = 24.3488071582° = 24°20'53″ = 0.42549540156 rad
Angle ∠ C = γ = 145.6555248542° = 145°39'19″ = 2.54221636599 rad

Height: ha = 10.71992510816
Height: hb = 4.51333688765
Height: hc = 3.2988231102

Median: ma = 22.41765117715
Median: mb = 16.72657286837
Median: mc = 6.59554529791

Inradius: r = 1.61880001633
Circumradius: R = 23.04326545773

Vertex coordinates: A[26; 0] B[0; 0] C[7.28884615385; 3.2988231102]
Centroid: CG[11.09661538462; 1.09994103673]
Coordinates of the circumscribed circle: U[13; -19.02553496674]
Coordinates of the inscribed circle: I[7.5; 1.61880001633]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.0033320124° = 170°12″ = 0.17444749781 rad
∠ B' = β' = 155.6521928418° = 155°39'7″ = 0.42549540156 rad
∠ C' = γ' = 34.34547514583° = 34°20'41″ = 2.54221636599 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+19+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-8)(26.5-19)(26.5-26) } ; ; T = sqrt{ 1838.44 } = 42.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.88 }{ 8 } = 10.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.88 }{ 19 } = 4.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.88 }{ 26 } = 3.3 ; ;

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{ 19**2+26**2-8**2 }{ 2 * 19 * 26 } ) = 9° 59'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+26**2-19**2 }{ 2 * 8 * 26 } ) = 24° 20'53" ; ; gamma = 180° - alpha - beta = 180° - 9° 59'48" - 24° 20'53" = 145° 39'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.88 }{ 26.5 } = 1.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 9° 59'48" } = 23.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 26**2 - 8**2 } }{ 2 } = 22.417 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 8**2 - 19**2 } }{ 2 } = 16.726 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 8**2 - 26**2 } }{ 2 } = 6.595 ; ;
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.