43 26.49 50.51 triangle

Obtuse scalene triangle.

Sides: a = 43   b = 26.49   c = 50.51

Area: T = 569.5354984
Perimeter: p = 120
Semiperimeter: s = 60

Angle ∠ A = α = 58.35551543243° = 58°21'19″ = 1.01884895785 rad
Angle ∠ B = β = 31.63112645432° = 31°37'53″ = 0.55220697128 rad
Angle ∠ C = γ = 90.01435811325° = 90°49″ = 1.57110333623 rad

Height: ha = 26.49899992558
Height: hb = 432.999998792
Height: hc = 22.55113753316

Median: ma = 34.12109627648
Median: mb = 44.9976666821
Median: mc = 25.2549653958

Inradius: r = 9.49222497333
Circumradius: R = 25.25550007095

Vertex coordinates: A[50.51; 0] B[0; 0] C[36.61219580281; 22.55113753316]
Centroid: CG[29.0410652676; 7.51771251105]
Coordinates of the circumscribed circle: U[25.255; -0.00659863311]
Coordinates of the inscribed circle: I[33.51; 9.49222497333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.6454845676° = 121°38'41″ = 1.01884895785 rad
∠ B' = β' = 148.3698735457° = 148°22'7″ = 0.55220697128 rad
∠ C' = γ' = 89.98664188675° = 89°59'11″ = 1.57110333623 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 = 43 ; ; b = 26.49 ; ; c = 50.51 ; ;

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

p = a+b+c = 43+26.49+50.51 = 120 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 120 }{ 2 } = 60 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60 * (60-43)(60-26.49)(60-50.51) } ; ; T = sqrt{ 324370.1 } = 569.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 569.53 }{ 43 } = 26.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 569.53 }{ 26.49 } = 43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 569.53 }{ 50.51 } = 22.55 ; ;

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{ 26.49**2+50.51**2-43**2 }{ 2 * 26.49 * 50.51 } ) = 58° 21'19" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 43**2+50.51**2-26.49**2 }{ 2 * 43 * 50.51 } ) = 31° 37'53" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 43**2+26.49**2-50.51**2 }{ 2 * 43 * 26.49 } ) = 90° 49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 569.53 }{ 60 } = 9.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 43 }{ 2 * sin 58° 21'19" } = 25.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 26.49**2+2 * 50.51**2 - 43**2 } }{ 2 } = 34.121 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 50.51**2+2 * 43**2 - 26.49**2 } }{ 2 } = 44.997 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 26.49**2+2 * 43**2 - 50.51**2 } }{ 2 } = 25.25 ; ;
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