10 14 22 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 14   c = 22

Area: T = 51.87548493974
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 19.68550548247° = 19°41'6″ = 0.34435690201 rad
Angle ∠ B = β = 28.13875265744° = 28°8'15″ = 0.49110924821 rad
Angle ∠ C = γ = 132.1777418601° = 132°10'39″ = 2.30769311514 rad

Height: ha = 10.37549698795
Height: hb = 7.41106927711
Height: hc = 4.71658953998

Median: ma = 17.74882393493
Median: mb = 15.58884572681
Median: mc = 5.19661524227

Inradius: r = 2.25554282347
Circumradius: R = 14.84334165871

Vertex coordinates: A[22; 0] B[0; 0] C[8.81881818182; 4.71658953998]
Centroid: CG[10.27327272727; 1.57219651333]
Coordinates of the circumscribed circle: U[11; -9.96662939942]
Coordinates of the inscribed circle: I[9; 2.25554282347]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.3154945175° = 160°18'54″ = 0.34435690201 rad
∠ B' = β' = 151.8622473426° = 151°51'45″ = 0.49110924821 rad
∠ C' = γ' = 47.82325813991° = 47°49'21″ = 2.30769311514 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 = 22 ; ;

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

p = a+b+c = 10+14+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-10)(23-14)(23-22) } ; ; T = sqrt{ 2691 } = 51.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.87 }{ 10 } = 10.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.87 }{ 14 } = 7.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.87 }{ 22 } = 4.72 ; ;

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**2-22**2 }{ 2 * 14 * 22 } ) = 19° 41'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-10**2-22**2 }{ 2 * 10 * 22 } ) = 28° 8'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-10**2-14**2 }{ 2 * 14 * 10 } ) = 132° 10'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.87 }{ 23 } = 2.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 19° 41'6" } = 14.84 ; ;




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