Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13.88   b = 12.6   c = 23.28

Area: T = 73.33298345832
Perimeter: p = 49.76
Semiperimeter: s = 24.88

Angle ∠ A = α = 29.99990231951° = 29°59'56″ = 0.52435817271 rad
Angle ∠ B = β = 26.99327072808° = 26°59'34″ = 0.47111116161 rad
Angle ∠ C = γ = 123.0088269524° = 123°30″ = 2.14768993104 rad

Height: ha = 10.56662585855
Height: hb = 11.6439656283
Height: hc = 6.32998139676

Median: ma = 17.38437740436
Median: mb = 18.11001767947
Median: mc = 6.34217347784

Inradius: r = 2.94773406183
Circumradius: R = 13.88804098739

Vertex coordinates: A[23.28; 0] B[0; 0] C[12.36879725086; 6.32998139676]
Centroid: CG[11.88326575029; 2.10999379892]
Coordinates of the circumscribed circle: U[11.64; -7.56114931242]
Coordinates of the inscribed circle: I[12.28; 2.94773406183]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0010976805° = 150°4″ = 0.52435817271 rad
∠ B' = β' = 153.0077292719° = 153°26″ = 0.47111116161 rad
∠ C' = γ' = 56.99217304759° = 56°59'30″ = 2.14768993104 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 = 13.88+12.6+23.28 = 49.76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49.76 }{ 2 } = 24.88 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.88 * (24.88-13.88)(24.88-12.6)(24.88-23.28) } ; ; T = sqrt{ 5377.26 } = 73.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73.33 }{ 13.88 } = 10.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73.33 }{ 12.6 } = 11.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73.33 }{ 23.28 } = 6.3 ; ;

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{ 12.6**2+23.28**2-13.88**2 }{ 2 * 12.6 * 23.28 } ) = 29° 59'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.88**2+23.28**2-12.6**2 }{ 2 * 13.88 * 23.28 } ) = 26° 59'34" ; ; gamma = 180° - alpha - beta = 180° - 29° 59'56" - 26° 59'34" = 123° 30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73.33 }{ 24.88 } = 2.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.88 }{ 2 * sin 29° 59'56" } = 13.88 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.6**2+2 * 23.28**2 - 13.88**2 } }{ 2 } = 17.384 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23.28**2+2 * 13.88**2 - 12.6**2 } }{ 2 } = 18.1 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.6**2+2 * 13.88**2 - 23.28**2 } }{ 2 } = 6.342 ; ;
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