39 80 89 triangle

Right scalene triangle.

Sides: a = 39   b = 80   c = 89

Area: T = 1560
Perimeter: p = 208
Semiperimeter: s = 104

Angle ∠ A = α = 25.98992335838° = 25°59'21″ = 0.45435976961 rad
Angle ∠ B = β = 64.01107664162° = 64°39″ = 1.11771986307 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 80
Height: hb = 39
Height: hc = 35.05661797753

Median: ma = 82.34222734687
Median: mb = 55.86659108939
Median: mc = 44.5

Inradius: r = 15
Circumradius: R = 44.5

Vertex coordinates: A[89; 0] B[0; 0] C[17.09898876404; 35.05661797753]
Centroid: CG[35.36332958801; 11.68553932584]
Coordinates of the circumscribed circle: U[44.5; 0]
Coordinates of the inscribed circle: I[24; 15]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.0110766416° = 154°39″ = 0.45435976961 rad
∠ B' = β' = 115.9899233584° = 115°59'21″ = 1.11771986307 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

a = 39 ; ; b = 80 ; ; c = 89 ; ;

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

p = a+b+c = 39+80+89 = 208 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 208 }{ 2 } = 104 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 104 * (104-39)(104-80)(104-89) } ; ; T = sqrt{ 2433600 } = 1560 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1560 }{ 39 } = 80 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1560 }{ 80 } = 39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1560 }{ 89 } = 35.06 ; ;

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{ 39**2-80**2-89**2 }{ 2 * 80 * 89 } ) = 25° 59'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 80**2-39**2-89**2 }{ 2 * 39 * 89 } ) = 64° 39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 89**2-39**2-80**2 }{ 2 * 80 * 39 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1560 }{ 104 } = 15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 39 }{ 2 * sin 25° 59'21" } = 44.5 ; ;




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