14 16 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 28

Area: T = 75.21997340421
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 19.61659069161° = 19°36'57″ = 0.34223621615 rad
Angle ∠ B = β = 22.56113280909° = 22°33'41″ = 0.39437694588 rad
Angle ∠ C = γ = 137.8232764993° = 137°49'22″ = 2.40554610333 rad

Height: ha = 10.74328191489
Height: hb = 9.43999667553
Height: hc = 5.37114095744

Median: ma = 21.70325344142
Median: mb = 20.64397674406
Median: mc = 5.47772255751

Inradius: r = 2.59330942773
Circumradius: R = 20.85111375735

Vertex coordinates: A[28; 0] B[0; 0] C[12.92985714286; 5.37114095744]
Centroid: CG[13.64328571429; 1.79904698581]
Coordinates of the circumscribed circle: U[14; -15.45221823089]
Coordinates of the inscribed circle: I[13; 2.59330942773]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.3844093084° = 160°23'3″ = 0.34223621615 rad
∠ B' = β' = 157.4398671909° = 157°26'19″ = 0.39437694588 rad
∠ C' = γ' = 42.17772350071° = 42°10'38″ = 2.40554610333 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 = 14 ; ; b = 16 ; ; c = 28 ; ;

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

p = a+b+c = 14+16+28 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-14)(29-16)(29-28) } ; ; T = sqrt{ 5655 } = 75.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.2 }{ 14 } = 10.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.2 }{ 16 } = 9.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.2 }{ 28 } = 5.37 ; ;

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{ 16**2+28**2-14**2 }{ 2 * 16 * 28 } ) = 19° 36'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+28**2-16**2 }{ 2 * 14 * 28 } ) = 22° 33'41" ; ; gamma = 180° - alpha - beta = 180° - 19° 36'57" - 22° 33'41" = 137° 49'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.2 }{ 29 } = 2.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 19° 36'57" } = 20.85 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 28**2 - 14**2 } }{ 2 } = 21.703 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 14**2 - 16**2 } }{ 2 } = 20.64 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 14**2 - 28**2 } }{ 2 } = 5.477 ; ;
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