10 14 19 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 14   c = 19

Area: T = 68.0887719157
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 30.79329879089° = 30°47'35″ = 0.53774390255 rad
Angle ∠ B = β = 45.78437484876° = 45°47'1″ = 0.7999077155 rad
Angle ∠ C = γ = 103.4233263603° = 103°25'24″ = 1.8055076473 rad

Height: ha = 13.61875438314
Height: hb = 9.72768170224
Height: hc = 7.16771283323

Median: ma = 15.92216833281
Median: mb = 13.47221935853
Median: mc = 7.59993420768

Inradius: r = 3.16768706585
Circumradius: R = 9.76768126974

Vertex coordinates: A[19; 0] B[0; 0] C[6.97436842105; 7.16771283323]
Centroid: CG[8.65878947368; 2.38990427774]
Coordinates of the circumscribed circle: U[9.5; -2.26772958048]
Coordinates of the inscribed circle: I[7.5; 3.16768706585]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.2077012091° = 149°12'25″ = 0.53774390255 rad
∠ B' = β' = 134.2166251512° = 134°12'59″ = 0.7999077155 rad
∠ C' = γ' = 76.57767363965° = 76°34'36″ = 1.8055076473 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 = 10 ; ; b = 14 ; ; c = 19 ; ;

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

p = a+b+c = 10+14+19 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-10)(21.5-14)(21.5-19) } ; ; T = sqrt{ 4635.94 } = 68.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 68.09 }{ 10 } = 13.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 68.09 }{ 14 } = 9.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 68.09 }{ 19 } = 7.17 ; ;

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{ 10**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 30° 47'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 45° 47'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-14**2 }{ 2 * 14 * 10 } ) = 103° 25'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 68.09 }{ 21.5 } = 3.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 30° 47'35" } = 9.77 ; ;




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