9 9 14 triangle

Obtuse isosceles triangle.

Sides: a = 9   b = 9   c = 14

Area: T = 39.59879797464
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ C = γ = 102.1155117462° = 102°6'54″ = 1.78222450158 rad

Height: ha = 8.87995510548
Height: hb = 8.87995510548
Height: hc = 5.65768542495

Median: ma = 10.87442815855
Median: mb = 10.87442815855
Median: mc = 5.65768542495

Inradius: r = 2.47548737342
Circumradius: R = 7.15994561595

Vertex coordinates: A[14; 0] B[0; 0] C[7; 5.65768542495]
Centroid: CG[7; 1.88656180832]
Coordinates of the circumscribed circle: U[7; -1.503260191]
Coordinates of the inscribed circle: I[7; 2.47548737342]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ C' = γ' = 77.8854882538° = 77°53'6″ = 1.78222450158 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 = 9 ; ; c = 14 ; ;

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

p = a+b+c = 9+9+14 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-9)(16-9)(16-14) } ; ; T = sqrt{ 1568 } = 39.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.6 }{ 9 } = 8.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.6 }{ 9 } = 8.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.6 }{ 14 } = 5.66 ; ;

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**2-9**2-14**2 }{ 2 * 9 * 14 } ) = 38° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-9**2-14**2 }{ 2 * 9 * 14 } ) = 38° 56'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-9**2-9**2 }{ 2 * 9 * 9 } ) = 102° 6'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.6 }{ 16 } = 2.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 38° 56'33" } = 7.16 ; ;




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