Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 4000   b = 6403.12   c = 5000

Area: T = 10000000.99999
Perimeter: p = 15403.12
Semiperimeter: s = 7701.56

Angle ∠ A = α = 38.66598385876° = 38°39'35″ = 0.67547414716 rad
Angle ∠ B = β = 909.9999222703° = 90° = 1.57107949702 rad
Angle ∠ C = γ = 51.34402391421° = 51°20'25″ = 0.89660562118 rad

Height: ha = 5000
Height: hb = 3123.477730481
Height: hc = 4000

Median: ma = 5385.162228792
Median: mb = 3201.564423743
Median: mc = 4716.988768996

Inradius: r = 1298.438823849
Circumradius: R = 3201.56

Vertex coordinates: A[5000; 0] B[0; 0] C[0.005542656; 4000]
Centroid: CG[1666.668847552; 1333.333333333]
Coordinates of the circumscribed circle: U[2500; 1999.99766084]
Coordinates of the inscribed circle: I[1298.44; 1298.438823849]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3440161412° = 141°20'25″ = 0.67547414716 rad
∠ B' = β' = 900.0000777297° = 90° = 1.57107949702 rad
∠ C' = γ' = 128.6659760858° = 128°39'35″ = 0.89660562118 rad

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How did we calculate this triangle?

a = 4000 ; ; b = 6403.12 ; ; c = 5000 ; ;

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

p = a+b+c = 4000+6403.12+5000 = 15403.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15403.12 }{ 2 } = 7701.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7701.56 * (7701.56-4000)(7701.56-6403.12)(7701.56-5000) } ; ; T = sqrt{ 10 * 10**{ 13 } } = 10000000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10000000 }{ 4000 } = 5000 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10000000 }{ 6403.12 } = 3123.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10000000 }{ 5000 } = 4000 ; ;

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{ 6403.12**2+5000**2-4000**2 }{ 2 * 6403.12 * 5000 } ) = 38° 39'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4000**2+5000**2-6403.12**2 }{ 2 * 4000 * 5000 } ) = 90° ; ; gamma = 180° - alpha - beta = 180° - 38° 39'35" - 90° = 51° 20'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10000000 }{ 7701.56 } = 1298.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4000 }{ 2 * sin 38° 39'35" } = 3201.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6403.12**2+2 * 5000**2 - 4000**2 } }{ 2 } = 5385.162 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5000**2+2 * 4000**2 - 6403.12**2 } }{ 2 } = 3201.564 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6403.12**2+2 * 4000**2 - 5000**2 } }{ 2 } = 4716.988 ; ;
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