Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 12.77   b = 6.72   c = 6.44

Area: T = 10.15498598517
Perimeter: p = 25.93
Semiperimeter: s = 12.965

Angle ∠ A = α = 152.0266248047° = 152°1'35″ = 2.65333585779 rad
Angle ∠ B = β = 14.29105221378° = 14°17'26″ = 0.24994166631 rad
Angle ∠ C = γ = 13.68332298148° = 13°41' = 0.23988174126 rad

Height: ha = 1.59896413237
Height: hb = 3.02107916225
Height: hc = 3.15221303887

Median: ma = 1.59661751157
Median: mb = 9.53985350028
Median: mc = 9.68223163551

Inradius: r = 0.78328661667
Circumradius: R = 13.61221272627

Vertex coordinates: A[6.44; 0] B[0; 0] C[12.37548524845; 3.15221303887]
Centroid: CG[6.27216174948; 1.05107101296]
Coordinates of the circumscribed circle: U[3.22; 13.22657933076]
Coordinates of the inscribed circle: I[6.245; 0.78328661667]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 27.97437519526° = 27°58'25″ = 2.65333585779 rad
∠ B' = β' = 165.7099477862° = 165°42'34″ = 0.24994166631 rad
∠ C' = γ' = 166.3176770185° = 166°19' = 0.23988174126 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 = 12.77+6.72+6.44 = 25.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.93 }{ 2 } = 12.97 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.97 * (12.97-12.77)(12.97-6.72)(12.97-6.44) } ; ; T = sqrt{ 103.02 } = 10.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.15 }{ 12.77 } = 1.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.15 }{ 6.72 } = 3.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.15 }{ 6.44 } = 3.15 ; ;

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{ 6.72**2+6.44**2-12.77**2 }{ 2 * 6.72 * 6.44 } ) = 152° 1'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.77**2+6.44**2-6.72**2 }{ 2 * 12.77 * 6.44 } ) = 14° 17'26" ; ; gamma = 180° - alpha - beta = 180° - 152° 1'35" - 14° 17'26" = 13° 41' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.15 }{ 12.97 } = 0.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.77 }{ 2 * sin 152° 1'35" } = 13.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.72**2+2 * 6.44**2 - 12.77**2 } }{ 2 } = 1.596 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.44**2+2 * 12.77**2 - 6.72**2 } }{ 2 } = 9.539 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.72**2+2 * 12.77**2 - 6.44**2 } }{ 2 } = 9.682 ; ;
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