Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 39.2   b = 28.6   c = 14.04

Area: T = 152.6699408186
Perimeter: p = 81.84
Semiperimeter: s = 40.92

Angle ∠ A = α = 130.4999480758° = 130°29'58″ = 2.27876456114 rad
Angle ∠ B = β = 33.69662709484° = 33°41'47″ = 0.58881108737 rad
Angle ∠ C = γ = 15.8044248294° = 15°48'15″ = 0.27658361685 rad

Height: ha = 7.78992555197
Height: hb = 10.67661823906
Height: hc = 21.74877789439

Median: ma = 11.10876910292
Median: mb = 25.73769539767
Median: mc = 33.5866003037

Inradius: r = 3.73109239537
Circumradius: R = 25.7765505694

Vertex coordinates: A[14.04; 0] B[0; 0] C[32.6144017094; 21.74877789439]
Centroid: CG[15.55113390313; 7.2499259648]
Coordinates of the circumscribed circle: U[7.02; 24.80111349293]
Coordinates of the inscribed circle: I[12.32; 3.73109239537]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 49.50105192423° = 49°30'2″ = 2.27876456114 rad
∠ B' = β' = 146.3043729052° = 146°18'13″ = 0.58881108737 rad
∠ C' = γ' = 164.1965751706° = 164°11'45″ = 0.27658361685 rad

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How did we calculate this triangle?

a = 39.2 ; ; b = 28.6 ; ; c = 14.04 ; ;

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

p = a+b+c = 39.2+28.6+14.04 = 81.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81.84 }{ 2 } = 40.92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.92 * (40.92-39.2)(40.92-28.6)(40.92-14.04) } ; ; T = sqrt{ 23307.95 } = 152.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 152.67 }{ 39.2 } = 7.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 152.67 }{ 28.6 } = 10.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 152.67 }{ 14.04 } = 21.75 ; ;

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{ 28.6**2+14.04**2-39.2**2 }{ 2 * 28.6 * 14.04 } ) = 130° 29'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 39.2**2+14.04**2-28.6**2 }{ 2 * 39.2 * 14.04 } ) = 33° 41'47" ; ; gamma = 180° - alpha - beta = 180° - 130° 29'58" - 33° 41'47" = 15° 48'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 152.67 }{ 40.92 } = 3.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 39.2 }{ 2 * sin 130° 29'58" } = 25.78 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.6**2+2 * 14.04**2 - 39.2**2 } }{ 2 } = 11.108 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.04**2+2 * 39.2**2 - 28.6**2 } }{ 2 } = 25.737 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.6**2+2 * 39.2**2 - 14.04**2 } }{ 2 } = 33.586 ; ;
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