458.1 482.1 843.8 triangle

Obtuse scalene triangle.

Sides: a = 458.1   b = 482.1   c = 843.8

Area: T = 87445.95661019
Perimeter: p = 1784
Semiperimeter: s = 892

Angle ∠ A = α = 25.46328240273° = 25°27'46″ = 0.44444101161 rad
Angle ∠ B = β = 26.90109369331° = 26°54'3″ = 0.47695099214 rad
Angle ∠ C = γ = 127.636623904° = 127°38'10″ = 2.22876726161 rad

Height: ha = 381.7776712953
Height: hb = 362.7711027181
Height: hc = 207.2677020863

Median: ma = 647.8787706439
Median: mb = 634.6832536785
Median: mc = 207.6987857476

Inradius: r = 98.03435830739
Circumradius: R = 532.7676884671

Vertex coordinates: A[843.8; 0] B[0; 0] C[408.5299059019; 207.2677020863]
Centroid: CG[417.4433019673; 69.08990069542]
Coordinates of the circumscribed circle: U[421.9; -325.3322050991]
Coordinates of the inscribed circle: I[409.9; 98.03435830739]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.5377175973° = 154°32'14″ = 0.44444101161 rad
∠ B' = β' = 153.0999063067° = 153°5'57″ = 0.47695099214 rad
∠ C' = γ' = 52.36437609605° = 52°21'50″ = 2.22876726161 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 = 458.1 ; ; b = 482.1 ; ; c = 843.8 ; ;

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

p = a+b+c = 458.1+482.1+843.8 = 1784 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1784 }{ 2 } = 892 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 892 * (892-458.1)(892-482.1)(892-843.8) } ; ; T = sqrt{ 7646795238.58 } = 87445.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87445.96 }{ 458.1 } = 381.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87445.96 }{ 482.1 } = 362.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87445.96 }{ 843.8 } = 207.27 ; ;

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{ 458.1**2-482.1**2-843.8**2 }{ 2 * 482.1 * 843.8 } ) = 25° 27'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 482.1**2-458.1**2-843.8**2 }{ 2 * 458.1 * 843.8 } ) = 26° 54'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 843.8**2-458.1**2-482.1**2 }{ 2 * 482.1 * 458.1 } ) = 127° 38'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87445.96 }{ 892 } = 98.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 458.1 }{ 2 * sin 25° 27'46" } = 532.77 ; ;

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