Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.81   b = 6.6   c = 12.79

Area: T = 21.13300373876
Perimeter: p = 27.2
Semiperimeter: s = 13.6

Angle ∠ A = α = 30.04216060772° = 30°2'30″ = 0.52443249386 rad
Angle ∠ B = β = 25.02883431816° = 25°1'42″ = 0.43768269948 rad
Angle ∠ C = γ = 124.9330050741° = 124°55'48″ = 2.18804407201 rad

Height: ha = 5.4111021098
Height: hb = 6.40330416326
Height: hc = 3.30441497088

Median: ma = 9.39880330389
Median: mb = 10.07697616655
Median: mc = 3.37437256854

Inradius: r = 1.55436792197
Circumradius: R = 7.88001913568

Vertex coordinates: A[12.79; 0] B[0; 0] C[7.07766301798; 3.30441497088]
Centroid: CG[6.62222100599; 1.10113832363]
Coordinates of the circumscribed circle: U[6.395; -4.46662019886]
Coordinates of the inscribed circle: I[7; 1.55436792197]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.9588393923° = 149°57'30″ = 0.52443249386 rad
∠ B' = β' = 154.9721656818° = 154°58'18″ = 0.43768269948 rad
∠ C' = γ' = 55.07699492588° = 55°4'12″ = 2.18804407201 rad

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How did we calculate this triangle?

a = 7.81 ; ; b = 6.6 ; ; c = 12.79 ; ;

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

p = a+b+c = 7.81+6.6+12.79 = 27.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.2 }{ 2 } = 13.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.6 * (13.6-7.81)(13.6-6.6)(13.6-12.79) } ; ; T = sqrt{ 446.48 } = 21.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.13 }{ 7.81 } = 5.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.13 }{ 6.6 } = 6.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.13 }{ 12.79 } = 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{ 6.6**2+12.79**2-7.81**2 }{ 2 * 6.6 * 12.79 } ) = 30° 2'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.81**2+12.79**2-6.6**2 }{ 2 * 7.81 * 12.79 } ) = 25° 1'42" ; ; gamma = 180° - alpha - beta = 180° - 30° 2'30" - 25° 1'42" = 124° 55'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.13 }{ 13.6 } = 1.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.81 }{ 2 * sin 30° 2'30" } = 7.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 12.79**2 - 7.81**2 } }{ 2 } = 9.398 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.79**2+2 * 7.81**2 - 6.6**2 } }{ 2 } = 10.07 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.6**2+2 * 7.81**2 - 12.79**2 } }{ 2 } = 3.374 ; ;
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