Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10.6   b = 8.1   c = 3.87

Area: T = 13.51215870468
Perimeter: p = 22.57
Semiperimeter: s = 11.285

Angle ∠ A = α = 120.4510681057° = 120°27'2″ = 2.10222609707 rad
Angle ∠ B = β = 41.20444832333° = 41°12'16″ = 0.7199153899 rad
Angle ∠ C = γ = 18.34548357097° = 18°20'41″ = 0.32201777839 rad

Height: ha = 2.54993560466
Height: hb = 3.33661943326
Height: hc = 6.98327323239

Median: ma = 3.49333436705
Median: mb = 6.87550236363
Median: mc = 9.2332593081

Inradius: r = 1.19773050108
Circumradius: R = 6.14880231532

Vertex coordinates: A[3.87; 0] B[0; 0] C[7.97550516796; 6.98327323239]
Centroid: CG[3.94883505599; 2.32875774413]
Coordinates of the circumscribed circle: U[1.935; 5.83655774086]
Coordinates of the inscribed circle: I[3.185; 1.19773050108]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 59.5499318943° = 59°32'58″ = 2.10222609707 rad
∠ B' = β' = 138.7965516767° = 138°47'44″ = 0.7199153899 rad
∠ C' = γ' = 161.655516429° = 161°39'19″ = 0.32201777839 rad

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How did we calculate this triangle?

a = 10.6 ; ; b = 8.1 ; ; c = 3.87 ; ;

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

p = a+b+c = 10.6+8.1+3.87 = 22.57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.57 }{ 2 } = 11.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.29 * (11.29-10.6)(11.29-8.1)(11.29-3.87) } ; ; T = sqrt{ 182.56 } = 13.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.51 }{ 10.6 } = 2.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.51 }{ 8.1 } = 3.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.51 }{ 3.87 } = 6.98 ; ;

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{ 8.1**2+3.87**2-10.6**2 }{ 2 * 8.1 * 3.87 } ) = 120° 27'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.6**2+3.87**2-8.1**2 }{ 2 * 10.6 * 3.87 } ) = 41° 12'16" ; ; gamma = 180° - alpha - beta = 180° - 120° 27'2" - 41° 12'16" = 18° 20'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.51 }{ 11.29 } = 1.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.6 }{ 2 * sin 120° 27'2" } = 6.15 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.1**2+2 * 3.87**2 - 10.6**2 } }{ 2 } = 3.493 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.87**2+2 * 10.6**2 - 8.1**2 } }{ 2 } = 6.875 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.1**2+2 * 10.6**2 - 3.87**2 } }{ 2 } = 9.233 ; ;
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