18 18 28 triangle

Obtuse isosceles triangle.

Sides: a = 18   b = 18   c = 28

Area: T = 158.3921918986
Perimeter: p = 64
Semiperimeter: s = 32

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 = 17.59991021095
Height: hb = 17.59991021095
Height: hc = 11.3143708499

Median: ma = 21.74985631709
Median: mb = 21.74985631709
Median: mc = 11.3143708499

Inradius: r = 4.95497474683
Circumradius: R = 14.3198912319

Vertex coordinates: A[28; 0] B[0; 0] C[14; 11.3143708499]
Centroid: CG[14; 3.77112361663]
Coordinates of the circumscribed circle: U[14; -3.005520382]
Coordinates of the inscribed circle: I[14; 4.95497474683]

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 = 18 ; ; b = 18 ; ; c = 28 ; ;

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

p = a+b+c = 18+18+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-18)(32-18)(32-28) } ; ; T = sqrt{ 25088 } = 158.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 158.39 }{ 18 } = 17.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 158.39 }{ 18 } = 17.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 158.39 }{ 28 } = 11.31 ; ;

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{ 18**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 38° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 38° 56'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-18**2 }{ 2 * 18 * 18 } ) = 102° 6'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 158.39 }{ 32 } = 4.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 38° 56'33" } = 14.32 ; ;




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