Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 11.18   b = 12.53   c = 21.4

Area: T = 54.50442416146
Perimeter: p = 45.11
Semiperimeter: s = 22.555

Angle ∠ A = α = 23.98772078514° = 23°59'14″ = 0.41986557554 rad
Angle ∠ B = β = 27.10549642289° = 27°6'18″ = 0.47330708694 rad
Angle ∠ C = γ = 128.908782792° = 128°54'28″ = 2.25498660288 rad

Height: ha = 9.7550311559
Height: hb = 8.76997991404
Height: hc = 5.09438543565

Median: ma = 16.6220239168
Median: mb = 15.8821623815
Median: mc = 5.14884609351

Inradius: r = 2.41765037293
Circumradius: R = 13.7550432403

Vertex coordinates: A[21.4; 0] B[0; 0] C[9.95221378505; 5.09438543565]
Centroid: CG[10.45107126168; 1.69879514522]
Coordinates of the circumscribed circle: U[10.7; -8.63662255222]
Coordinates of the inscribed circle: I[10.025; 2.41765037293]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0132792149° = 156°46″ = 0.41986557554 rad
∠ B' = β' = 152.8955035771° = 152°53'42″ = 0.47330708694 rad
∠ C' = γ' = 51.09221720804° = 51°5'32″ = 2.25498660288 rad

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How did we calculate this triangle?

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

p = a+b+c = 11.18+12.53+21.4 = 45.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45.11 }{ 2 } = 22.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.56 * (22.56-11.18)(22.56-12.53)(22.56-21.4) } ; ; T = sqrt{ 2970.71 } = 54.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.5 }{ 11.18 } = 9.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.5 }{ 12.53 } = 8.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.5 }{ 21.4 } = 5.09 ; ;

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{ 12.53**2+21.4**2-11.18**2 }{ 2 * 12.53 * 21.4 } ) = 23° 59'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11.18**2+21.4**2-12.53**2 }{ 2 * 11.18 * 21.4 } ) = 27° 6'18" ; ;
 gamma = 180° - alpha - beta = 180° - 23° 59'14" - 27° 6'18" = 128° 54'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.5 }{ 22.56 } = 2.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11.18 }{ 2 * sin 23° 59'14" } = 13.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.53**2+2 * 21.4**2 - 11.18**2 } }{ 2 } = 16.62 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 21.4**2+2 * 11.18**2 - 12.53**2 } }{ 2 } = 15.882 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.53**2+2 * 11.18**2 - 21.4**2 } }{ 2 } = 5.148 ; ;
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