9 22 30 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 22   c = 30

Area: T = 52.79114529067
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 9.20553928801° = 9°12'19″ = 0.16106644147 rad
Angle ∠ B = β = 23.02197122554° = 23°1'11″ = 0.40217697717 rad
Angle ∠ C = γ = 147.7754894865° = 147°46'30″ = 2.57991584672 rad

Height: ha = 11.73114339793
Height: hb = 4.79992229915
Height: hc = 3.51994301938

Median: ma = 25.91881403654
Median: mb = 19.22223827867
Median: mc = 7.58328754441

Inradius: r = 1.73108673084
Circumradius: R = 28.13295535212

Vertex coordinates: A[30; 0] B[0; 0] C[8.28333333333; 3.51994301938]
Centroid: CG[12.76111111111; 1.17331433979]
Coordinates of the circumscribed circle: U[15; -23.79664657313]
Coordinates of the inscribed circle: I[8.5; 1.73108673084]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.795460712° = 170°47'41″ = 0.16106644147 rad
∠ B' = β' = 156.9880287745° = 156°58'49″ = 0.40217697717 rad
∠ C' = γ' = 32.22551051355° = 32°13'30″ = 2.57991584672 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 = 22 ; ; c = 30 ; ;

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

p = a+b+c = 9+22+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-9)(30.5-22)(30.5-30) } ; ; T = sqrt{ 2786.94 } = 52.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.79 }{ 9 } = 11.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.79 }{ 22 } = 4.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.79 }{ 30 } = 3.52 ; ;

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**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 9° 12'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-9**2-30**2 }{ 2 * 9 * 30 } ) = 23° 1'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-9**2-22**2 }{ 2 * 22 * 9 } ) = 147° 46'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.79 }{ 30.5 } = 1.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 9° 12'19" } = 28.13 ; ;




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