7 19 22 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 19   c = 22

Area: T = 63.87548776907
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 17.79655541818° = 17°47'44″ = 0.31105910127 rad
Angle ∠ B = β = 56.05219105004° = 56°3'7″ = 0.97882903903 rad
Angle ∠ C = γ = 106.1532535318° = 106°9'9″ = 1.85327112506 rad

Height: ha = 18.25499650545
Height: hb = 6.72436713359
Height: hc = 5.80768070628

Median: ma = 20.25546291005
Median: mb = 13.27659180474
Median: mc = 9.16551513899

Inradius: r = 2.66114532371
Circumradius: R = 11.45220767232

Vertex coordinates: A[22; 0] B[0; 0] C[3.90990909091; 5.80768070628]
Centroid: CG[8.63663636364; 1.93656023543]
Coordinates of the circumscribed circle: U[11; -3.18659160809]
Coordinates of the inscribed circle: I[5; 2.66114532371]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.2044445818° = 162°12'16″ = 0.31105910127 rad
∠ B' = β' = 123.94880895° = 123°56'53″ = 0.97882903903 rad
∠ C' = γ' = 73.84774646822° = 73°50'51″ = 1.85327112506 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 = 19 ; ; c = 22 ; ;

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

p = a+b+c = 7+19+22 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-7)(24-19)(24-22) } ; ; T = sqrt{ 4080 } = 63.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.87 }{ 7 } = 18.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.87 }{ 19 } = 6.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.87 }{ 22 } = 5.81 ; ;

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**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 17° 47'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-7**2-22**2 }{ 2 * 7 * 22 } ) = 56° 3'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-7**2-19**2 }{ 2 * 19 * 7 } ) = 106° 9'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.87 }{ 24 } = 2.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 17° 47'44" } = 11.45 ; ;




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