Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 1.06   b = 0.87   c = 0.4

Area: T = 0.16661496144
Perimeter: p = 2.33
Semiperimeter: s = 1.165

Angle ∠ A = α = 107.2766470416° = 107°16'35″ = 1.87223276187 rad
Angle ∠ B = β = 51.60328724113° = 51°36'10″ = 0.90106400271 rad
Angle ∠ C = γ = 21.12106571729° = 21°7'14″ = 0.36986250079 rad

Height: ha = 0.31334898385
Height: hb = 0.38219531366
Height: hc = 0.83107480721

Median: ma = 0.42113668236
Median: mb = 0.67327369471
Median: mc = 0.94988150505

Inradius: r = 0.14326176948
Circumradius: R = 0.5555041914

Vertex coordinates: A[0.4; 0] B[0; 0] C[0.6588375; 0.83107480721]
Centroid: CG[0.35327916667; 0.2776916024]
Coordinates of the circumscribed circle: U[0.2; 0.51877562421]
Coordinates of the inscribed circle: I[0.295; 0.14326176948]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 72.72435295842° = 72°43'25″ = 1.87223276187 rad
∠ B' = β' = 128.3977127589° = 128°23'50″ = 0.90106400271 rad
∠ C' = γ' = 158.8799342827° = 158°52'46″ = 0.36986250079 rad

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How did we calculate this triangle?

a = 1.06 ; ; b = 0.87 ; ; c = 0.4 ; ;

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

p = a+b+c = 1.06+0.87+0.4 = 2.33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2.33 }{ 2 } = 1.17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.17 * (1.17-1.06)(1.17-0.87)(1.17-0.4) } ; ; T = sqrt{ 0.03 } = 0.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.17 }{ 1.06 } = 0.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.17 }{ 0.87 } = 0.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.17 }{ 0.4 } = 0.83 ; ;

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{ 0.87**2+0.4**2-1.06**2 }{ 2 * 0.87 * 0.4 } ) = 107° 16'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.06**2+0.4**2-0.87**2 }{ 2 * 1.06 * 0.4 } ) = 51° 36'10" ; ; gamma = 180° - alpha - beta = 180° - 107° 16'35" - 51° 36'10" = 21° 7'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.17 }{ 1.17 } = 0.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.06 }{ 2 * sin 107° 16'35" } = 0.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.87**2+2 * 0.4**2 - 1.06**2 } }{ 2 } = 0.421 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.4**2+2 * 1.06**2 - 0.87**2 } }{ 2 } = 0.673 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.87**2+2 * 1.06**2 - 0.4**2 } }{ 2 } = 0.949 ; ;
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