7 14 19 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 14   c = 19

Area: T = 39.49768353163
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 17.27656260544° = 17°16'32″ = 0.3021516555 rad
Angle ∠ B = β = 36.43769168605° = 36°26'13″ = 0.63659441685 rad
Angle ∠ C = γ = 126.2877457085° = 126°17'15″ = 2.20441319301 rad

Height: ha = 11.28548100904
Height: hb = 5.64224050452
Height: hc = 4.15875616122

Median: ma = 16.31771688721
Median: mb = 12.49899959968
Median: mc = 5.67989083458

Inradius: r = 1.97548417658
Circumradius: R = 11.78657543844

Vertex coordinates: A[19; 0] B[0; 0] C[5.63215789474; 4.15875616122]
Centroid: CG[8.21105263158; 1.38658538707]
Coordinates of the circumscribed circle: U[9.5; -6.97552423908]
Coordinates of the inscribed circle: I[6; 1.97548417658]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.7244373946° = 162°43'28″ = 0.3021516555 rad
∠ B' = β' = 143.5633083139° = 143°33'47″ = 0.63659441685 rad
∠ C' = γ' = 53.71325429149° = 53°42'45″ = 2.20441319301 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 = 7 ; ; b = 14 ; ; c = 19 ; ;

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

p = a+b+c = 7+14+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-7)(20-14)(20-19) } ; ; T = sqrt{ 1560 } = 39.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.5 }{ 7 } = 11.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.5 }{ 14 } = 5.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.5 }{ 19 } = 4.16 ; ;

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{ 7**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 17° 16'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-7**2-19**2 }{ 2 * 7 * 19 } ) = 36° 26'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-7**2-14**2 }{ 2 * 14 * 7 } ) = 126° 17'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.5 }{ 20 } = 1.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 17° 16'32" } = 11.79 ; ;




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