Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 20   b = 22   c = 23

Area: T = 201.304434049
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 52.71985213296° = 52°43'7″ = 0.9220111774 rad
Angle ∠ B = β = 61.07329496159° = 61°4'23″ = 1.06659240547 rad
Angle ∠ C = γ = 66.20985290545° = 66°12'31″ = 1.15655568249 rad

Height: ha = 20.1330434049
Height: hb = 18.330039459
Height: hc = 17.505472526

Median: ma = 20.16218451537
Median: mb = 18.53437529929
Median: mc = 17.65997159068

Inradius: r = 6.19439797074
Circumradius: R = 12.56880350153

Vertex coordinates: A[23; 0] B[0; 0] C[9.67439130435; 17.505472526]
Centroid: CG[10.89113043478; 5.835490842]
Coordinates of the circumscribed circle: U[11.5; 5.077005958]
Coordinates of the inscribed circle: I[10.5; 6.19439797074]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.281147867° = 127°16'53″ = 0.9220111774 rad
∠ B' = β' = 118.9277050384° = 118°55'37″ = 1.06659240547 rad
∠ C' = γ' = 113.7911470945° = 113°47'29″ = 1.15655568249 rad

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How did we calculate this triangle?

a = 20 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 20+22+23 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-20)(32.5-22)(32.5-23) } ; ; T = sqrt{ 40523.44 } = 201.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 201.3 }{ 20 } = 20.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 201.3 }{ 22 } = 18.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 201.3 }{ 23 } = 17.5 ; ;

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{ 22**2+23**2-20**2 }{ 2 * 22 * 23 } ) = 52° 43'7" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 20**2+23**2-22**2 }{ 2 * 20 * 23 } ) = 61° 4'23" ; ; gamma = 180° - alpha - beta = 180° - 52° 43'7" - 61° 4'23" = 66° 12'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 201.3 }{ 32.5 } = 6.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 20 }{ 2 * sin 52° 43'7" } = 12.57 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 23**2 - 20**2 } }{ 2 } = 20.162 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 20**2 - 22**2 } }{ 2 } = 18.534 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 22**2+2 * 20**2 - 23**2 } }{ 2 } = 17.6 ; ;
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