10 20 23 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 20   c = 23

Area: T = 99.73768412373
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 25.69986873132° = 25°41'55″ = 0.44985267071 rad
Angle ∠ B = β = 60.14437210096° = 60°8'37″ = 1.0549705956 rad
Angle ∠ C = γ = 94.15875916772° = 94°9'27″ = 1.64333599905 rad

Height: ha = 19.94773682475
Height: hb = 9.97436841237
Height: hc = 8.67327688032

Median: ma = 20.96442552932
Median: mb = 14.64658185159
Median: mc = 10.85112672071

Inradius: r = 3.76436543863
Circumradius: R = 11.53303431083

Vertex coordinates: A[23; 0] B[0; 0] C[4.97882608696; 8.67327688032]
Centroid: CG[9.32660869565; 2.89109229344]
Coordinates of the circumscribed circle: U[11.5; -0.83659498753]
Coordinates of the inscribed circle: I[6.5; 3.76436543863]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.3011312687° = 154°18'5″ = 0.44985267071 rad
∠ B' = β' = 119.856627899° = 119°51'23″ = 1.0549705956 rad
∠ C' = γ' = 85.84224083228° = 85°50'33″ = 1.64333599905 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 = 10 ; ; b = 20 ; ; c = 23 ; ;

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

p = a+b+c = 10+20+23 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-10)(26.5-20)(26.5-23) } ; ; T = sqrt{ 9947.44 } = 99.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 99.74 }{ 10 } = 19.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 99.74 }{ 20 } = 9.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 99.74 }{ 23 } = 8.67 ; ;

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{ 10**2-20**2-23**2 }{ 2 * 20 * 23 } ) = 25° 41'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-10**2-23**2 }{ 2 * 10 * 23 } ) = 60° 8'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-10**2-20**2 }{ 2 * 20 * 10 } ) = 94° 9'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 99.74 }{ 26.5 } = 3.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 25° 41'55" } = 11.53 ; ;




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