18 20 26 triangle

Acute scalene triangle.

Sides: a = 18   b = 20   c = 26

Area: T = 179.6599554565
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 43.69108952793° = 43°41'27″ = 0.76325499758 rad
Angle ∠ B = β = 50.132165845° = 50°7'54″ = 0.87549624994 rad
Angle ∠ C = γ = 86.17774462707° = 86°10'39″ = 1.50440801784 rad

Height: ha = 19.95655060628
Height: hb = 17.96599554565
Height: hc = 13.81553503512

Median: ma = 21.37875583264
Median: mb = 20
Median: mc = 13.89224439894

Inradius: r = 5.61224860802
Circumradius: R = 13.02989855432

Vertex coordinates: A[26; 0] B[0; 0] C[11.53884615385; 13.81553503512]
Centroid: CG[12.51328205128; 4.60551167837]
Coordinates of the circumscribed circle: U[13; 0.86985990362]
Coordinates of the inscribed circle: I[12; 5.61224860802]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.3099104721° = 136°18'33″ = 0.76325499758 rad
∠ B' = β' = 129.868834155° = 129°52'6″ = 0.87549624994 rad
∠ C' = γ' = 93.82325537293° = 93°49'21″ = 1.50440801784 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 = 20 ; ; c = 26 ; ;

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

p = a+b+c = 18+20+26 = 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)(32-20)(32-26) } ; ; T = sqrt{ 32256 } = 179.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 179.6 }{ 18 } = 19.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 179.6 }{ 20 } = 17.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 179.6 }{ 26 } = 13.82 ; ;

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**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 43° 41'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 50° 7'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-18**2-20**2 }{ 2 * 20 * 18 } ) = 86° 10'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 179.6 }{ 32 } = 5.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 43° 41'27" } = 13.03 ; ;




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