673 861 989 triangle

Acute scalene triangle.

Sides: a = 673   b = 861   c = 989

Area: T = 284643.5687927
Perimeter: p = 2523
Semiperimeter: s = 1261.5

Angle ∠ A = α = 41.95550183447° = 41°57'18″ = 0.73222532079 rad
Angle ∠ B = β = 58.79332291994° = 58°47'36″ = 1.02661354274 rad
Angle ∠ C = γ = 79.25217524559° = 79°15'6″ = 1.38332040183 rad

Height: ha = 845.8954704092
Height: hb = 661.1932956857
Height: hc = 575.6198944241

Median: ma = 863.9965804388
Median: mb = 728.1454731492
Median: mc = 593.7976892885

Inradius: r = 225.6398975765
Circumradius: R = 503.333037663

Vertex coordinates: A[989; 0] B[0; 0] C[348.7700202225; 575.6198944241]
Centroid: CG[445.9900067408; 191.8732981414]
Coordinates of the circumscribed circle: U[494.5; 93.86880884996]
Coordinates of the inscribed circle: I[400.5; 225.6398975765]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0454981655° = 138°2'42″ = 0.73222532079 rad
∠ B' = β' = 121.2076770801° = 121°12'24″ = 1.02661354274 rad
∠ C' = γ' = 100.7488247544° = 100°44'54″ = 1.38332040183 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 = 673 ; ; b = 861 ; ; c = 989 ; ;

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

p = a+b+c = 673+861+989 = 2523 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2523 }{ 2 } = 1261.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1261.5 * (1261.5-673)(1261.5-861)(1261.5-989) } ; ; T = sqrt{ 81021960762.2 } = 284643.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 284643.57 }{ 673 } = 845.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 284643.57 }{ 861 } = 661.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 284643.57 }{ 989 } = 575.62 ; ;

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{ 673**2-861**2-989**2 }{ 2 * 861 * 989 } ) = 41° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 861**2-673**2-989**2 }{ 2 * 673 * 989 } ) = 58° 47'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 989**2-673**2-861**2 }{ 2 * 861 * 673 } ) = 79° 15'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 284643.57 }{ 1261.5 } = 225.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 673 }{ 2 * sin 41° 57'18" } = 503.33 ; ;




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