Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13.88   b = 12.6   c = 1.46

Area: T = 4.64220348458
Perimeter: p = 27.94
Semiperimeter: s = 13.97

Angle ∠ A = α = 149.6989972745° = 149°41'24″ = 2.61325828816 rad
Angle ∠ B = β = 27.26770044631° = 27°16'1″ = 0.4765899005 rad
Angle ∠ C = γ = 3.04330227919° = 3°2'35″ = 0.05331107669 rad

Height: ha = 0.66988811017
Height: hb = 0.73768309279
Height: hc = 6.35989518436

Median: ma = 5.68217426904
Median: mb = 7.59662490744
Median: mc = 13.23553428365

Inradius: r = 0.33222859589
Circumradius: R = 13.75113228832

Vertex coordinates: A[1.46; 0] B[0; 0] C[12.33876712329; 6.35989518436]
Centroid: CG[4.59992237443; 2.12196506145]
Coordinates of the circumscribed circle: U[0.73; 13.73219328951]
Coordinates of the inscribed circle: I[1.37; 0.33222859589]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.3110027255° = 30°18'36″ = 2.61325828816 rad
∠ B' = β' = 152.7332995537° = 152°43'59″ = 0.4765899005 rad
∠ C' = γ' = 176.9576977208° = 176°57'25″ = 0.05331107669 rad

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How did we calculate this triangle?

a = 13.88 ; ; b = 12.6 ; ; c = 1.46 ; ;

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

p = a+b+c = 13.88+12.6+1.46 = 27.94 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.94 }{ 2 } = 13.97 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.97 * (13.97-13.88)(13.97-12.6)(13.97-1.46) } ; ; T = sqrt{ 21.55 } = 4.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.64 }{ 13.88 } = 0.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.64 }{ 12.6 } = 0.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.64 }{ 1.46 } = 6.36 ; ;

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{ 12.6**2+1.46**2-13.88**2 }{ 2 * 12.6 * 1.46 } ) = 149° 41'24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.88**2+1.46**2-12.6**2 }{ 2 * 13.88 * 1.46 } ) = 27° 16'1" ; ; gamma = 180° - alpha - beta = 180° - 149° 41'24" - 27° 16'1" = 3° 2'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.64 }{ 13.97 } = 0.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.88 }{ 2 * sin 149° 41'24" } = 13.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.6**2+2 * 1.46**2 - 13.88**2 } }{ 2 } = 5.682 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.46**2+2 * 13.88**2 - 12.6**2 } }{ 2 } = 7.596 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.6**2+2 * 13.88**2 - 1.46**2 } }{ 2 } = 13.235 ; ;
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