20 26 30 triangle

Acute scalene triangle.

Sides: a = 20   b = 26   c = 30

Area: T = 256.2549878049
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 41.07553488744° = 41°4'31″ = 0.71769000793 rad
Angle ∠ B = β = 58.66877485024° = 58°40'4″ = 1.02439453761 rad
Angle ∠ C = γ = 80.25769026232° = 80°15'25″ = 1.40107471982 rad

Height: ha = 25.62549878049
Height: hb = 19.71215290807
Height: hc = 17.08333252033

Median: ma = 26.23297540972
Median: mb = 21.93217121995
Median: mc = 17.6921806013

Inradius: r = 6.74334178434
Circumradius: R = 15.22195194382

Vertex coordinates: A[30; 0] B[0; 0] C[10.4; 17.08333252033]
Centroid: CG[13.46766666667; 5.69444417344]
Coordinates of the circumscribed circle: U[15; 2.57656109818]
Coordinates of the inscribed circle: I[12; 6.74334178434]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.9254651126° = 138°55'29″ = 0.71769000793 rad
∠ B' = β' = 121.3322251498° = 121°19'56″ = 1.02439453761 rad
∠ C' = γ' = 99.74330973768° = 99°44'35″ = 1.40107471982 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 = 20 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 20+26+30 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-20)(38-26)(38-30) } ; ; T = sqrt{ 65664 } = 256.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 256.25 }{ 20 } = 25.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 256.25 }{ 26 } = 19.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 256.25 }{ 30 } = 17.08 ; ;

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{ 20**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 41° 4'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-20**2-30**2 }{ 2 * 20 * 30 } ) = 58° 40'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-20**2-26**2 }{ 2 * 26 * 20 } ) = 80° 15'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 256.25 }{ 38 } = 6.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 41° 4'31" } = 15.22 ; ;




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