9 19 22 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 19   c = 22

Area: T = 84.85328137424
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 23.95334516247° = 23°57'12″ = 0.41880665981 rad
Angle ∠ B = β = 58.99224169931° = 58°59'33″ = 1.03296119102 rad
Angle ∠ C = γ = 97.05441313821° = 97°3'15″ = 1.69439141453 rad

Height: ha = 18.85661808316
Height: hb = 8.93218751308
Height: hc = 7.71438921584

Median: ma = 20.05661711201
Median: mb = 13.86554246239
Median: mc = 10

Inradius: r = 3.39441125497
Circumradius: R = 11.08438987951

Vertex coordinates: A[22; 0] B[0; 0] C[4.63663636364; 7.71438921584]
Centroid: CG[8.87987878788; 2.57112973861]
Coordinates of the circumscribed circle: U[11; -1.36111805538]
Coordinates of the inscribed circle: I[6; 3.39441125497]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0476548375° = 156°2'48″ = 0.41880665981 rad
∠ B' = β' = 121.0087583007° = 121°27″ = 1.03296119102 rad
∠ C' = γ' = 82.94658686179° = 82°56'45″ = 1.69439141453 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 = 9 ; ; b = 19 ; ; c = 22 ; ;

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

p = a+b+c = 9+19+22 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-9)(25-19)(25-22) } ; ; T = sqrt{ 7200 } = 84.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 84.85 }{ 9 } = 18.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 84.85 }{ 19 } = 8.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 84.85 }{ 22 } = 7.71 ; ;

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{ 9**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 23° 57'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-9**2-22**2 }{ 2 * 9 * 22 } ) = 58° 59'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-9**2-19**2 }{ 2 * 19 * 9 } ) = 97° 3'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 84.85 }{ 25 } = 3.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 23° 57'12" } = 11.08 ; ;




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