6 23 24 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 23   c = 24

Area: T = 68.94551774963
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 14.46657584676° = 14°27'57″ = 0.25224751141 rad
Angle ∠ B = β = 73.25501091195° = 73°15' = 1.27884555816 rad
Angle ∠ C = γ = 92.28441324129° = 92°17'3″ = 1.6110661958 rad

Height: ha = 22.98217258321
Height: hb = 5.99552328258
Height: hc = 5.7455431458

Median: ma = 23.31330864537
Median: mb = 13.18114263265
Median: mc = 11.76986022959

Inradius: r = 2.60217048112
Circumradius: R = 12.01095419298

Vertex coordinates: A[24; 0] B[0; 0] C[1.72991666667; 5.7455431458]
Centroid: CG[8.57663888889; 1.91551438193]
Coordinates of the circumscribed circle: U[12; -0.47986411639]
Coordinates of the inscribed circle: I[3.5; 2.60217048112]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.5344241532° = 165°32'3″ = 0.25224751141 rad
∠ B' = β' = 106.7549890881° = 106°45' = 1.27884555816 rad
∠ C' = γ' = 87.71658675871° = 87°42'57″ = 1.6110661958 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 = 23 ; ; c = 24 ; ;

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

p = a+b+c = 6+23+24 = 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 * (26.5-6)(26.5-23)(26.5-24) } ; ; T = sqrt{ 4753.44 } = 68.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 68.95 }{ 6 } = 22.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 68.95 }{ 23 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 68.95 }{ 24 } = 5.75 ; ;

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**2-23**2-24**2 }{ 2 * 23 * 24 } ) = 14° 27'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-6**2-24**2 }{ 2 * 6 * 24 } ) = 73° 15' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-6**2-23**2 }{ 2 * 23 * 6 } ) = 92° 17'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 68.95 }{ 26.5 } = 2.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 14° 27'57" } = 12.01 ; ;




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