70 50 80 triangle

Acute scalene triangle.

Sides: a = 70   b = 50   c = 80

Area: T = 1732.051080757
Perimeter: p = 200
Semiperimeter: s = 100

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ C = γ = 81.78767892983° = 81°47'12″ = 1.42774487579 rad

Height: ha = 49.48771659305
Height: hb = 69.28220323028
Height: hc = 43.30112701892

Median: ma = 56.7899083458
Median: mb = 70.88772343938
Median: mc = 45.82657569496

Inradius: r = 17.32105080757
Circumradius: R = 40.41545188433

Vertex coordinates: A[80; 0] B[0; 0] C[55; 43.30112701892]
Centroid: CG[45; 14.43437567297]
Coordinates of the circumscribed circle: U[40; 5.77435026919]
Coordinates of the inscribed circle: I[50; 17.32105080757]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ C' = γ' = 98.21332107017° = 98°12'48″ = 1.42774487579 rad

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How did we calculate this triangle?

a = 70 ; ; b = 50 ; ; c = 80 ; ;

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

p = a+b+c = 70+50+80 = 200 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 200 }{ 2 } = 100 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 100 * (100-70)(100-50)(100-80) } ; ; T = sqrt{ 3000000 } = 1732.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1732.05 }{ 70 } = 49.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1732.05 }{ 50 } = 69.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1732.05 }{ 80 } = 43.3 ; ;

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{ 50**2+80**2-70**2 }{ 2 * 50 * 80 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 70**2+80**2-50**2 }{ 2 * 70 * 80 } ) = 38° 12'48" ; ; gamma = 180° - alpha - beta = 180° - 60° - 38° 12'48" = 81° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1732.05 }{ 100 } = 17.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 70 }{ 2 * sin 60° } = 40.41 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 80**2 - 70**2 } }{ 2 } = 56.789 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 70**2 - 50**2 } }{ 2 } = 70.887 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 70**2 - 80**2 } }{ 2 } = 45.826 ; ;
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