Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 8.49   b = 16.97   c = 18.97

Area: T = 72.03876326306
Perimeter: p = 44.43
Semiperimeter: s = 22.215

Angle ∠ A = α = 26.58765165307° = 26°35'11″ = 0.46440222501 rad
Angle ∠ B = β = 63.45332712969° = 63°27'12″ = 1.10774685053 rad
Angle ∠ C = γ = 89.96602121724° = 89°57'37″ = 1.57701018982 rad

Height: ha = 16.97699959083
Height: hb = 8.49899979529
Height: hc = 7.59549006463

Median: ma = 17.49900221555
Median: mb = 11.99989697474
Median: mc = 9.49902726515

Inradius: r = 3.24327473613
Circumradius: R = 9.4855002287

Vertex coordinates: A[18.97; 0] B[0; 0] C[3.79444148656; 7.59549006463]
Centroid: CG[7.58881382885; 2.53216335488]
Coordinates of the circumscribed circle: U[9.485; 0.00765866563]
Coordinates of the inscribed circle: I[5.245; 3.24327473613]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4133483469° = 153°24'49″ = 0.46440222501 rad
∠ B' = β' = 116.5476728703° = 116°32'48″ = 1.10774685053 rad
∠ C' = γ' = 90.04397878276° = 90°2'23″ = 1.57701018982 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 = 8.49+16.97+18.97 = 44.43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44.43 }{ 2 } = 22.22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.22 * (22.22-8.49)(22.22-16.97)(22.22-18.97) } ; ; T = sqrt{ 5189.42 } = 72.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 72.04 }{ 8.49 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 72.04 }{ 16.97 } = 8.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 72.04 }{ 18.97 } = 7.59 ; ;

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{ 16.97**2+18.97**2-8.49**2 }{ 2 * 16.97 * 18.97 } ) = 26° 35'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.49**2+18.97**2-16.97**2 }{ 2 * 8.49 * 18.97 } ) = 63° 27'12" ; ; gamma = 180° - alpha - beta = 180° - 26° 35'11" - 63° 27'12" = 89° 57'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 72.04 }{ 22.22 } = 3.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.49 }{ 2 * sin 26° 35'11" } = 9.49 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.97**2+2 * 18.97**2 - 8.49**2 } }{ 2 } = 17.49 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.97**2+2 * 8.49**2 - 16.97**2 } }{ 2 } = 11.999 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.97**2+2 * 8.49**2 - 18.97**2 } }{ 2 } = 9.49 ; ;
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