921 70 923.656 triangle

Right scalene triangle.

Sides: a = 921   b = 70   c = 923.656

Area: T = 322354.9999997
Perimeter: p = 1914.656
Semiperimeter: s = 957.328

Angle ∠ A = α = 85.65438905184° = 85°39'14″ = 1.49549424067 rad
Angle ∠ B = β = 4.34663732822° = 4°20'47″ = 0.07658585243 rad
Angle ∠ C = γ = 909.9997361995° = 89°59'59″ = 1.57107917226 rad

Height: ha = 709.9999999993
Height: hb = 9210.99999999
Height: hc = 69.799871294

Median: ma = 465.7989601825
Median: mb = 921.6654637039
Median: mc = 461.8288321366

Inradius: r = 33.67218449681
Circumradius: R = 461.8288000005

Vertex coordinates: A[923.656; 0] B[0; 0] C[918.351131604; 69.799871294]
Centroid: CG[614.002243868; 23.26662376467]
Coordinates of the circumscribed circle: U[461.828; 0.00221263429]
Coordinates of the inscribed circle: I[887.328; 33.67218449681]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 94.34661094816° = 94°20'46″ = 1.49549424067 rad
∠ B' = β' = 175.6543626718° = 175°39'13″ = 0.07658585243 rad
∠ C' = γ' = 900.0002638005° = 90°1″ = 1.57107917226 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 = 921 ; ; b = 70 ; ; c = 923.66 ; ;

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

p = a+b+c = 921+70+923.66 = 1914.66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1914.66 }{ 2 } = 957.33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 957.33 * (957.33-921)(957.33-70)(957.33-923.66) } ; ; T = sqrt{ 1039095224.98 } = 32235 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32235 }{ 921 } = 70 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32235 }{ 70 } = 921 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32235 }{ 923.66 } = 69.8 ; ;

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{ 921**2-70**2-923.66**2 }{ 2 * 70 * 923.66 } ) = 85° 39'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 70**2-921**2-923.66**2 }{ 2 * 921 * 923.66 } ) = 4° 20'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 923.66**2-921**2-70**2 }{ 2 * 70 * 921 } ) = 89° 59'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32235 }{ 957.33 } = 33.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 921 }{ 2 * sin 85° 39'14" } = 461.83 ; ;




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