Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 5   b = 11   c = 12

Area: T = 27.49554541697
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 24.62199773287° = 24°37'12″ = 0.43296996662 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 88.95882011495° = 88°57'30″ = 1.55326135067 rad

Height: ha = 10.99881816679
Height: hb = 4.99991734854
Height: hc = 4.5832575695

Median: ma = 11.23661025271
Median: mb = 7.36554599313
Median: mc = 6.08327625303

Inradius: r = 1.96439610121
Circumradius: R = 6.00109919815

Vertex coordinates: A[12; 0] B[0; 0] C[2; 4.5832575695]
Centroid: CG[4.66766666667; 1.52875252317]
Coordinates of the circumscribed circle: U[6; 0.10991089451]
Coordinates of the inscribed circle: I[3; 1.96439610121]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.3880022671° = 155°22'48″ = 0.43296996662 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 91.04217988505° = 91°2'30″ = 1.55326135067 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 = 5+11+12 = 28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28 }{ 2 } = 14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14 * (14-5)(14-11)(14-12) } ; ; T = sqrt{ 756 } = 27.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.5 }{ 5 } = 11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.5 }{ 11 } = 5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.5 }{ 12 } = 4.58 ; ;

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{ 11**2+12**2-5**2 }{ 2 * 11 * 12 } ) = 24° 37'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+12**2-11**2 }{ 2 * 5 * 12 } ) = 66° 25'19" ; ; gamma = 180° - alpha - beta = 180° - 24° 37'12" - 66° 25'19" = 88° 57'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.5 }{ 14 } = 1.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 24° 37'12" } = 6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 12**2 - 5**2 } }{ 2 } = 11.236 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 12**2+2 * 5**2 - 11**2 } }{ 2 } = 7.365 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 5**2 - 12**2 } }{ 2 } = 6.083 ; ;
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