9 14 21 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 14   c = 21

Area: T = 47.83330429724
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 18.98994985755° = 18°59'22″ = 0.33114292734 rad
Angle ∠ B = β = 30.40990349246° = 30°24'33″ = 0.53107377818 rad
Angle ∠ C = γ = 130.60114665° = 130°36'5″ = 2.27994255984 rad

Height: ha = 10.6329565105
Height: hb = 6.83332918532
Height: hc = 4.55655279021

Median: ma = 17.27699160392
Median: mb = 14.56602197786
Median: mc = 5.31550729064

Inradius: r = 2.1744229226
Circumradius: R = 13.82993522405

Vertex coordinates: A[21; 0] B[0; 0] C[7.76219047619; 4.55655279021]
Centroid: CG[9.58773015873; 1.51985093007]
Coordinates of the circumscribed circle: U[10.5; -99.0000546327]
Coordinates of the inscribed circle: I[8; 2.1744229226]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.0110501425° = 161°38″ = 0.33114292734 rad
∠ B' = β' = 149.5910965075° = 149°35'27″ = 0.53107377818 rad
∠ C' = γ' = 49.39985335° = 49°23'55″ = 2.27994255984 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 = 14 ; ; c = 21 ; ;

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

p = a+b+c = 9+14+21 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-9)(22-14)(22-21) } ; ; T = sqrt{ 2288 } = 47.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.83 }{ 9 } = 10.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.83 }{ 14 } = 6.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.83 }{ 21 } = 4.56 ; ;

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**2-14**2-21**2 }{ 2 * 14 * 21 } ) = 18° 59'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-9**2-21**2 }{ 2 * 9 * 21 } ) = 30° 24'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 21**2-9**2-14**2 }{ 2 * 14 * 9 } ) = 130° 36'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.83 }{ 22 } = 2.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 18° 59'22" } = 13.83 ; ;




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