6 19 24 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 19   c = 24

Area: T = 35.30549217532
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 8.9087873456° = 8°54'28″ = 0.15554717212 rad
Angle ∠ B = β = 29.3633334592° = 29°21'48″ = 0.5122486868 rad
Angle ∠ C = γ = 141.7298791952° = 141°43'44″ = 2.47436340644 rad

Height: ha = 11.76883072511
Height: hb = 3.7166307553
Height: hc = 2.94220768128

Median: ma = 21.43659511102
Median: mb = 14.68884308216
Median: mc = 7.38224115301

Inradius: r = 1.44110172144
Circumradius: R = 19.37440692808

Vertex coordinates: A[24; 0] B[0; 0] C[5.22991666667; 2.94220768128]
Centroid: CG[9.74330555556; 0.98106922709]
Coordinates of the circumscribed circle: U[12; -15.21103438652]
Coordinates of the inscribed circle: I[5.5; 1.44110172144]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.0922126544° = 171°5'32″ = 0.15554717212 rad
∠ B' = β' = 150.6376665408° = 150°38'12″ = 0.5122486868 rad
∠ C' = γ' = 38.27112080479° = 38°16'16″ = 2.47436340644 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 = 19 ; ; c = 24 ; ;

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

p = a+b+c = 6+19+24 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-6)(24.5-19)(24.5-24) } ; ; T = sqrt{ 1246.44 } = 35.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.3 }{ 6 } = 11.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.3 }{ 19 } = 3.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.3 }{ 24 } = 2.94 ; ;

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**2-19**2-24**2 }{ 2 * 19 * 24 } ) = 8° 54'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-6**2-24**2 }{ 2 * 6 * 24 } ) = 29° 21'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-6**2-19**2 }{ 2 * 19 * 6 } ) = 141° 43'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.3 }{ 24.5 } = 1.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 8° 54'28" } = 19.37 ; ;




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