Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 39.2   b = 28.6   c = 51.18

Area: T = 556.6387516842
Perimeter: p = 118.98
Semiperimeter: s = 59.49

Angle ∠ A = α = 49.51440044174° = 49°30'50″ = 0.86441824029 rad
Angle ∠ B = β = 33.70439501787° = 33°42'14″ = 0.58882449015 rad
Angle ∠ C = γ = 96.78220454039° = 96°46'55″ = 1.68991653491 rad

Height: ha = 28.43998733083
Height: hb = 38.92657004785
Height: hc = 21.75221499352

Median: ma = 36.53110306452
Median: mb = 43.28442488672
Median: mc = 22.8577206741

Inradius: r = 9.35768249595
Circumradius: R = 25.77703262284

Vertex coordinates: A[51.18; 0] B[0; 0] C[32.6111101993; 21.75221499352]
Centroid: CG[27.9330367331; 7.25107166451]
Coordinates of the circumscribed circle: U[25.59; -3.04332899827]
Coordinates of the inscribed circle: I[30.89; 9.35768249595]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.4865995583° = 130°29'10″ = 0.86441824029 rad
∠ B' = β' = 146.2966049821° = 146°17'46″ = 0.58882449015 rad
∠ C' = γ' = 83.21879545961° = 83°13'5″ = 1.68991653491 rad

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How did we calculate this triangle?

a = 39.2 ; ; b = 28.6 ; ; c = 51.18 ; ;

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

p = a+b+c = 39.2+28.6+51.18 = 118.98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 118.98 }{ 2 } = 59.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.49 * (59.49-39.2)(59.49-28.6)(59.49-51.18) } ; ; T = sqrt{ 309845.33 } = 556.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 556.64 }{ 39.2 } = 28.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 556.64 }{ 28.6 } = 38.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 556.64 }{ 51.18 } = 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+51.18**2-39.2**2 }{ 2 * 28.6 * 51.18 } ) = 49° 30'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 39.2**2+51.18**2-28.6**2 }{ 2 * 39.2 * 51.18 } ) = 33° 42'14" ; ; gamma = 180° - alpha - beta = 180° - 49° 30'50" - 33° 42'14" = 96° 46'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 556.64 }{ 59.49 } = 9.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 39.2 }{ 2 * sin 49° 30'50" } = 25.77 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.6**2+2 * 51.18**2 - 39.2**2 } }{ 2 } = 36.531 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 51.18**2+2 * 39.2**2 - 28.6**2 } }{ 2 } = 43.284 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28.6**2+2 * 39.2**2 - 51.18**2 } }{ 2 } = 22.857 ; ;
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