6 21 23 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 21   c = 23

Area: T = 61.64441400297
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 14.78987097356° = 14°47'19″ = 0.2588111677 rad
Angle ∠ B = β = 63.30327985505° = 63°18'10″ = 1.10548422604 rad
Angle ∠ C = γ = 101.9088491714° = 101°54'31″ = 1.77986387161 rad

Height: ha = 20.54880466766
Height: hb = 5.8710870479
Height: hc = 5.36603600026

Median: ma = 21.81774242293
Median: mb = 13.12444047484
Median: mc = 10.3087764064

Inradius: r = 2.46657656012
Circumradius: R = 11.75329419609

Vertex coordinates: A[23; 0] B[0; 0] C[2.69656521739; 5.36603600026]
Centroid: CG[8.56552173913; 1.78767866675]
Coordinates of the circumscribed circle: U[11.5; -2.42552102459]
Coordinates of the inscribed circle: I[4; 2.46657656012]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.2111290264° = 165°12'41″ = 0.2588111677 rad
∠ B' = β' = 116.6977201449° = 116°41'50″ = 1.10548422604 rad
∠ C' = γ' = 78.09215082861° = 78°5'29″ = 1.77986387161 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6 ; ; b = 21 ; ; c = 23 ; ;

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

p = a+b+c = 6+21+23 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-6)(25-21)(25-23) } ; ; T = sqrt{ 3800 } = 61.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.64 }{ 6 } = 20.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.64 }{ 21 } = 5.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.64 }{ 23 } = 5.36 ; ;

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{ 6**2-21**2-23**2 }{ 2 * 21 * 23 } ) = 14° 47'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-6**2-23**2 }{ 2 * 6 * 23 } ) = 63° 18'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-6**2-21**2 }{ 2 * 21 * 6 } ) = 101° 54'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.64 }{ 25 } = 2.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 14° 47'19" } = 11.75 ; ;




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