14 19 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 19   c = 28

Area: T = 120.2854818244
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 26.88548293213° = 26°53'5″ = 0.46992287905 rad
Angle ∠ B = β = 37.85773792467° = 37°51'27″ = 0.6610735914 rad
Angle ∠ C = γ = 115.2587791432° = 115°15'28″ = 2.01216279491 rad

Height: ha = 17.18435454634
Height: hb = 12.66215598152
Height: hc = 8.59217727317

Median: ma = 22.88801223773
Median: mb = 19.99437490231
Median: mc = 9.08329510623

Inradius: r = 3.94437645326
Circumradius: R = 15.48799252905

Vertex coordinates: A[28; 0] B[0; 0] C[11.05435714286; 8.59217727317]
Centroid: CG[13.01878571429; 2.86439242439]
Coordinates of the circumscribed circle: U[14; -6.6055156092]
Coordinates of the inscribed circle: I[11.5; 3.94437645326]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.1155170679° = 153°6'55″ = 0.46992287905 rad
∠ B' = β' = 142.1432620753° = 142°8'33″ = 0.6610735914 rad
∠ C' = γ' = 64.7422208568° = 64°44'32″ = 2.01216279491 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 = 19 ; ; c = 28 ; ;

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

p = a+b+c = 14+19+28 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-14)(30.5-19)(30.5-28) } ; ; T = sqrt{ 14468.44 } = 120.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 120.28 }{ 14 } = 17.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 120.28 }{ 19 } = 12.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 120.28 }{ 28 } = 8.59 ; ;

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{ 14**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 26° 53'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 37° 51'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 115° 15'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 120.28 }{ 30.5 } = 3.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 26° 53'5" } = 15.48 ; ;




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