717 856 792 triangle

Acute scalene triangle.

Sides: a = 717   b = 856   c = 792

Area: T = 264918.6487571
Perimeter: p = 2365
Semiperimeter: s = 1182.5

Angle ∠ A = α = 51.40105320808° = 51°24'2″ = 0.89771085221 rad
Angle ∠ B = β = 68.91330558516° = 68°54'47″ = 1.20327597222 rad
Angle ∠ C = γ = 59.68664120676° = 59°41'11″ = 1.04217244093 rad

Height: ha = 738.9644149431
Height: hb = 618.9698802736
Height: hc = 668.9866483766

Median: ma = 742.6155479235
Median: mb = 622.4898955725
Median: mc = 683.0798692392

Inradius: r = 224.0332682935
Circumradius: R = 458.7187787948

Vertex coordinates: A[792; 0] B[0; 0] C[257.9655277778; 668.9866483766]
Centroid: CG[349.9888425926; 222.9955494589]
Coordinates of the circumscribed circle: U[396; 231.5329715112]
Coordinates of the inscribed circle: I[326.5; 224.0332682935]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.5999467919° = 128°35'58″ = 0.89771085221 rad
∠ B' = β' = 111.0876944148° = 111°5'13″ = 1.20327597222 rad
∠ C' = γ' = 120.3143587932° = 120°18'49″ = 1.04217244093 rad

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How did we calculate this triangle?

a = 717 ; ; b = 856 ; ; c = 792 ; ;

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

p = a+b+c = 717+856+792 = 2365 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2365 }{ 2 } = 1182.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1182.5 * (1182.5-717)(1182.5-856)(1182.5-792) } ; ; T = sqrt{ 70181889830.9 } = 264918.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 264918.65 }{ 717 } = 738.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 264918.65 }{ 856 } = 618.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 264918.65 }{ 792 } = 668.99 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 856**2+792**2-717**2 }{ 2 * 856 * 792 } ) = 51° 24'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 717**2+792**2-856**2 }{ 2 * 717 * 792 } ) = 68° 54'47" ; ; gamma = 180° - alpha - beta = 180° - 51° 24'2" - 68° 54'47" = 59° 41'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 264918.65 }{ 1182.5 } = 224.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 717 }{ 2 * sin 51° 24'2" } = 458.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 856**2+2 * 792**2 - 717**2 } }{ 2 } = 742.615 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 792**2+2 * 717**2 - 856**2 } }{ 2 } = 622.489 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 856**2+2 * 717**2 - 792**2 } }{ 2 } = 683.079 ; ;
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