60 80 100 triangle

Right scalene Pythagorean triangle.

Sides: a = 60   b = 80   c = 100

Area: T = 2400
Perimeter: p = 240
Semiperimeter: s = 120

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 80
Height: hb = 60
Height: hc = 48

Median: ma = 85.44400374532
Median: mb = 72.11110255093
Median: mc = 50

Inradius: r = 20
Circumradius: R = 50

Vertex coordinates: A[100; 0] B[0; 0] C[36; 48]
Centroid: CG[45.33333333333; 16]
Coordinates of the circumscribed circle: U[50; 0]
Coordinates of the inscribed circle: I[40; 20]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 60 ; ; b = 80 ; ; c = 100 ; ;

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

p = a+b+c = 60+80+100 = 240 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 240 }{ 2 } = 120 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 120 * (120-60)(120-80)(120-100) } ; ; T = sqrt{ 5760000 } = 2400 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2400 }{ 60 } = 80 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2400 }{ 80 } = 60 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2400 }{ 100 } = 48 ; ;

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{ 80**2+100**2-60**2 }{ 2 * 80 * 100 } ) = 36° 52'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 60**2+100**2-80**2 }{ 2 * 60 * 100 } ) = 53° 7'48" ; ; gamma = 180° - alpha - beta = 180° - 36° 52'12" - 53° 7'48" = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2400 }{ 120 } = 20 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 36° 52'12" } = 50 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 100**2 - 60**2 } }{ 2 } = 85.44 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 60**2 - 80**2 } }{ 2 } = 72.111 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 60**2 - 100**2 } }{ 2 } = 50 ; ;
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