8 20 23 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 20   c = 23

Area: T = 78.33222251695
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 19.91219034612° = 19°54'43″ = 0.34875282757 rad
Angle ∠ B = β = 58.3688336233° = 58°22'6″ = 1.01987196462 rad
Angle ∠ C = γ = 101.7219760306° = 101°43'11″ = 1.77553447317 rad

Height: ha = 19.58330562924
Height: hb = 7.83332225169
Height: hc = 6.81114978408

Median: ma = 21.17878185845
Median: mb = 14.01878457689
Median: mc = 9.98774921777

Inradius: r = 3.07218519674
Circumradius: R = 11.74548470027

Vertex coordinates: A[23; 0] B[0; 0] C[4.19656521739; 6.81114978408]
Centroid: CG[9.06552173913; 2.27704992803]
Coordinates of the circumscribed circle: U[11.5; -2.38656720474]
Coordinates of the inscribed circle: I[5.5; 3.07218519674]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.0888096539° = 160°5'17″ = 0.34875282757 rad
∠ B' = β' = 121.6321663767° = 121°37'54″ = 1.01987196462 rad
∠ C' = γ' = 78.28802396942° = 78°16'49″ = 1.77553447317 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 = 8 ; ; b = 20 ; ; c = 23 ; ;

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

p = a+b+c = 8+20+23 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-8)(25.5-20)(25.5-23) } ; ; T = sqrt{ 6135.94 } = 78.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.33 }{ 8 } = 19.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.33 }{ 20 } = 7.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.33 }{ 23 } = 6.81 ; ;

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{ 8**2-20**2-23**2 }{ 2 * 20 * 23 } ) = 19° 54'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-8**2-23**2 }{ 2 * 8 * 23 } ) = 58° 22'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-8**2-20**2 }{ 2 * 20 * 8 } ) = 101° 43'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.33 }{ 25.5 } = 3.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 19° 54'43" } = 11.74 ; ;




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