Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13.2   b = 5.3   c = 9.33

Area: T = 19.82440295834
Perimeter: p = 27.83
Semiperimeter: s = 13.915

Angle ∠ A = α = 126.6987953853° = 126°41'53″ = 2.21112964503 rad
Angle ∠ B = β = 18.78799035164° = 18°46'48″ = 0.32877711496 rad
Angle ∠ C = γ = 34.52221426307° = 34°31'20″ = 0.60325250537 rad

Height: ha = 3.0043640846
Height: hb = 7.48107658805
Height: hc = 4.25495240265

Median: ma = 3.74329199831
Median: mb = 11.11985408215
Median: mc = 8.91108234749

Inradius: r = 1.42546517847
Circumradius: R = 8.23215101132

Vertex coordinates: A[9.33; 0] B[0; 0] C[12.4977261522; 4.25495240265]
Centroid: CG[7.27657538407; 1.41765080088]
Coordinates of the circumscribed circle: U[4.665; 6.78220007183]
Coordinates of the inscribed circle: I[8.615; 1.42546517847]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 53.30220461471° = 53°18'7″ = 2.21112964503 rad
∠ B' = β' = 161.2220096484° = 161°13'12″ = 0.32877711496 rad
∠ C' = γ' = 145.4787857369° = 145°28'40″ = 0.60325250537 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 = 13.2+5.3+9.33 = 27.83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.83 }{ 2 } = 13.92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.92 * (13.92-13.2)(13.92-5.3)(13.92-9.33) } ; ; T = sqrt{ 392.99 } = 19.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.82 }{ 13.2 } = 3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.82 }{ 5.3 } = 7.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.82 }{ 9.33 } = 4.25 ; ;

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{ 5.3**2+9.33**2-13.2**2 }{ 2 * 5.3 * 9.33 } ) = 126° 41'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.2**2+9.33**2-5.3**2 }{ 2 * 13.2 * 9.33 } ) = 18° 46'48" ; ; gamma = 180° - alpha - beta = 180° - 126° 41'53" - 18° 46'48" = 34° 31'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.82 }{ 13.92 } = 1.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.2 }{ 2 * sin 126° 41'53" } = 8.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.3**2+2 * 9.33**2 - 13.2**2 } }{ 2 } = 3.743 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.33**2+2 * 13.2**2 - 5.3**2 } }{ 2 } = 11.119 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.3**2+2 * 13.2**2 - 9.33**2 } }{ 2 } = 8.911 ; ;
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.