23979 5901 22080 triangle

Obtuse scalene triangle.

Sides: a = 23979   b = 5901   c = 22080

Area: T = 63803787.66553
Perimeter: p = 51960
Semiperimeter: s = 25980

Angle ∠ A = α = 101.6555157419° = 101°39'19″ = 1.77442171986 rad
Angle ∠ B = β = 13.94765278495° = 13°56'48″ = 0.24334128302 rad
Angle ∠ C = γ = 64.39883147315° = 64°23'54″ = 1.12439626248 rad

Height: ha = 5321.639873934
Height: hb = 21624.73773887
Height: hc = 5779.329859287

Median: ma = 10836.32773414
Median: mb = 22859.43994124
Median: mc = 13528.69325089

Inradius: r = 2455.881097249
Circumradius: R = 12241.91332886

Vertex coordinates: A[22080; 0] B[0; 0] C[23272.125; 5779.329859287]
Centroid: CG[15117.375; 1926.443286429]
Coordinates of the circumscribed circle: U[11040; 5289.88109972]
Coordinates of the inscribed circle: I[20079; 2455.881097249]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 78.3454842581° = 78°20'41″ = 1.77442171986 rad
∠ B' = β' = 166.0533472151° = 166°3'12″ = 0.24334128302 rad
∠ C' = γ' = 115.6021685268° = 115°36'6″ = 1.12439626248 rad

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How did we calculate this triangle?

a = 23979 ; ; b = 5901 ; ; c = 22080 ; ;

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

p = a+b+c = 23979+5901+22080 = 51960 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51960 }{ 2 } = 25980 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25980 * (25980-23979)(25980-5901)(25980-22080) } ; ; T = sqrt{ 4.071 * 10**{ 15 } } = 63803787.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63803787.67 }{ 23979 } = 5321.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63803787.67 }{ 5901 } = 21624.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63803787.67 }{ 22080 } = 5779.33 ; ;

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{ 23979**2-5901**2-22080**2 }{ 2 * 5901 * 22080 } ) = 101° 39'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5901**2-23979**2-22080**2 }{ 2 * 23979 * 22080 } ) = 13° 56'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22080**2-23979**2-5901**2 }{ 2 * 5901 * 23979 } ) = 64° 23'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63803787.67 }{ 25980 } = 2455.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23979 }{ 2 * sin 101° 39'19" } = 12241.91 ; ;




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