Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 5   b = 14   c = 16

Area: T = 33.88986042793
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 17.61224390704° = 17°36'45″ = 0.30773950511 rad
Angle ∠ B = β = 57.91100487437° = 57°54'36″ = 1.01107210206 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 13.55554417117
Height: hb = 4.84112291828
Height: hc = 4.23660755349

Median: ma = 14.82439670804
Median: mb = 9.56655632349
Median: mc = 6.81990908485

Inradius: r = 1.93664916731
Circumradius: R = 8.26223644719

Vertex coordinates: A[16; 0] B[0; 0] C[2.656625; 4.23660755349]
Centroid: CG[6.219875; 1.41220251783]
Coordinates of the circumscribed circle: U[8; -2.0665591118]
Coordinates of the inscribed circle: I[3.5; 1.93664916731]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.388756093° = 162°23'15″ = 0.30773950511 rad
∠ B' = β' = 122.0989951256° = 122°5'24″ = 1.01107210206 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 rad

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How did we calculate this triangle?

a = 5 ; ; b = 14 ; ; c = 16 ; ;

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

p = a+b+c = 5+14+16 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-5)(17.5-14)(17.5-16) } ; ; T = sqrt{ 1148.44 } = 33.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.89 }{ 5 } = 13.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.89 }{ 14 } = 4.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.89 }{ 16 } = 4.24 ; ;

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{ 14**2+16**2-5**2 }{ 2 * 14 * 16 } ) = 17° 36'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+16**2-14**2 }{ 2 * 5 * 16 } ) = 57° 54'36" ; ; gamma = 180° - alpha - beta = 180° - 17° 36'45" - 57° 54'36" = 104° 28'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.89 }{ 17.5 } = 1.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 17° 36'45" } = 8.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 16**2 - 5**2 } }{ 2 } = 14.824 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 5**2 - 14**2 } }{ 2 } = 9.566 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 5**2 - 16**2 } }{ 2 } = 6.819 ; ;
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