18 19 28 triangle

Obtuse scalene triangle.

Sides: a = 18   b = 19   c = 28

Area: T = 169.1999401595
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 39.50107243938° = 39°30'3″ = 0.68994176976 rad
Angle ∠ B = β = 42.17772350071° = 42°10'38″ = 0.73661316203 rad
Angle ∠ C = γ = 98.32220405992° = 98°19'19″ = 1.71660433357 rad

Height: ha = 18.87999335105
Height: hb = 17.81104633258
Height: hc = 12.08656715425

Median: ma = 22.17697992774
Median: mb = 21.53548554674
Median: mc = 12.10437184369

Inradius: r = 5.20661354337
Circumradius: R = 14.14989862106

Vertex coordinates: A[28; 0] B[0; 0] C[13.33992857143; 12.08656715425]
Centroid: CG[13.78797619048; 4.02985571808]
Coordinates of the circumscribed circle: U[14; -2.04878795831]
Coordinates of the inscribed circle: I[13.5; 5.20661354337]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.4999275606° = 140°29'57″ = 0.68994176976 rad
∠ B' = β' = 137.8232764993° = 137°49'22″ = 0.73661316203 rad
∠ C' = γ' = 81.67879594008° = 81°40'41″ = 1.71660433357 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 = 18 ; ; b = 19 ; ; c = 28 ; ;

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

p = a+b+c = 18+19+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-18)(32.5-19)(32.5-28) } ; ; T = sqrt{ 28628.44 } = 169.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 169.2 }{ 18 } = 18.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 169.2 }{ 19 } = 17.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 169.2 }{ 28 } = 12.09 ; ;

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{ 18**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 39° 30'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 42° 10'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-19**2 }{ 2 * 19 * 18 } ) = 98° 19'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 169.2 }{ 32.5 } = 5.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 39° 30'3" } = 14.15 ; ;




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