Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.7   b = 9.32   c = 5.8

Area: T = 25.03107014362
Perimeter: p = 27.82
Semiperimeter: s = 13.91

Angle ∠ A = α = 112.1654788661° = 112°9'53″ = 1.95876448669 rad
Angle ∠ B = β = 42.81545851443° = 42°48'53″ = 0.74772554786 rad
Angle ∠ C = γ = 25.02106261947° = 25°1'14″ = 0.4376692308 rad

Height: ha = 3.94218427459
Height: hb = 5.3711395158
Height: hc = 8.63112763573

Median: ma = 4.46441572553
Median: mb = 8.70334131236
Median: mc = 10.75548221743

Inradius: r = 1.7999475301
Circumradius: R = 6.85766915888

Vertex coordinates: A[5.8; 0] B[0; 0] C[9.31661724138; 8.63112763573]
Centroid: CG[5.03987241379; 2.87770921191]
Coordinates of the circumscribed circle: U[2.9; 6.21332293974]
Coordinates of the inscribed circle: I[4.59; 1.7999475301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 67.8355211339° = 67°50'7″ = 1.95876448669 rad
∠ B' = β' = 137.1855414856° = 137°11'7″ = 0.74772554786 rad
∠ C' = γ' = 154.9799373805° = 154°58'46″ = 0.4376692308 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 = 12.7+9.32+5.8 = 27.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.82 }{ 2 } = 13.91 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.91 * (13.91-12.7)(13.91-9.32)(13.91-5.8) } ; ; T = sqrt{ 626.54 } = 25.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.03 }{ 12.7 } = 3.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.03 }{ 9.32 } = 5.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.03 }{ 5.8 } = 8.63 ; ;

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{ 9.32**2+5.8**2-12.7**2 }{ 2 * 9.32 * 5.8 } ) = 112° 9'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.7**2+5.8**2-9.32**2 }{ 2 * 12.7 * 5.8 } ) = 42° 48'53" ; ; gamma = 180° - alpha - beta = 180° - 112° 9'53" - 42° 48'53" = 25° 1'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.03 }{ 13.91 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.7 }{ 2 * sin 112° 9'53" } = 6.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.32**2+2 * 5.8**2 - 12.7**2 } }{ 2 } = 4.464 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.8**2+2 * 12.7**2 - 9.32**2 } }{ 2 } = 8.703 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.32**2+2 * 12.7**2 - 5.8**2 } }{ 2 } = 10.755 ; ;
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