Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 9.43   b = 7.21   c = 4.12

Area: T = 13.98986974447
Perimeter: p = 20.76
Semiperimeter: s = 10.38

Angle ∠ A = α = 109.6387972411° = 109°38'17″ = 1.91435436038 rad
Angle ∠ B = β = 46.06334975537° = 46°3'49″ = 0.80439596973 rad
Angle ∠ C = γ = 24.29985300356° = 24°17'55″ = 0.42440893525 rad

Height: ha = 2.96768499353
Height: hb = 3.88803599014
Height: hc = 6.79106298275

Median: ma = 3.54997178458
Median: mb = 6.32108879914
Median: mc = 8.13770080496

Inradius: r = 1.34876587134
Circumradius: R = 5.00661851203

Vertex coordinates: A[4.12; 0] B[0; 0] C[6.54331067961; 6.79106298275]
Centroid: CG[3.5544368932; 2.26435432758]
Coordinates of the circumscribed circle: U[2.06; 4.56327063744]
Coordinates of the inscribed circle: I[3.17; 1.34876587134]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 70.36220275893° = 70°21'43″ = 1.91435436038 rad
∠ B' = β' = 133.9376502446° = 133°56'11″ = 0.80439596973 rad
∠ C' = γ' = 155.7011469964° = 155°42'5″ = 0.42440893525 rad

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How did we calculate this triangle?

a = 9.43 ; ; b = 7.21 ; ; c = 4.12 ; ;

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

p = a+b+c = 9.43+7.21+4.12 = 20.76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.76 }{ 2 } = 10.38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.38 * (10.38-9.43)(10.38-7.21)(10.38-4.12) } ; ; T = sqrt{ 195.68 } = 13.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.99 }{ 9.43 } = 2.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.99 }{ 7.21 } = 3.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.99 }{ 4.12 } = 6.79 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 9.43**2-7.21**2-4.12**2 }{ 2 * 7.21 * 4.12 } ) = 109° 38'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.21**2-9.43**2-4.12**2 }{ 2 * 9.43 * 4.12 } ) = 46° 3'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.12**2-9.43**2-7.21**2 }{ 2 * 7.21 * 9.43 } ) = 24° 17'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.99 }{ 10.38 } = 1.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.43 }{ 2 * sin 109° 38'17" } = 5.01 ; ;




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