26 27 30 triangle

Acute scalene triangle.

Sides: a = 26   b = 27   c = 30

Area: T = 327.5098683091
Perimeter: p = 83
Semiperimeter: s = 41.5

Angle ∠ A = α = 53.96655482592° = 53°57'56″ = 0.94218764998 rad
Angle ∠ B = β = 57.11554026449° = 57°6'55″ = 0.99768518298 rad
Angle ∠ C = γ = 68.91990490959° = 68°55'9″ = 1.20328643241 rad

Height: ha = 25.19329756224
Height: hb = 24.26599024512
Height: hc = 21.83439122061

Median: ma = 25.40766920318
Median: mb = 24.61219889485
Median: mc = 21.85217733834

Inradius: r = 7.89217754962
Circumradius: R = 16.07659096532

Vertex coordinates: A[30; 0] B[0; 0] C[14.11766666667; 21.83439122061]
Centroid: CG[14.70655555556; 7.27879707354]
Coordinates of the circumscribed circle: U[15; 5.78222894408]
Coordinates of the inscribed circle: I[14.5; 7.89217754962]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.0344451741° = 126°2'4″ = 0.94218764998 rad
∠ B' = β' = 122.8854597355° = 122°53'5″ = 0.99768518298 rad
∠ C' = γ' = 111.0810950904° = 111°4'51″ = 1.20328643241 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 = 26 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 26+27+30 = 83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 83 }{ 2 } = 41.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41.5 * (41.5-26)(41.5-27)(41.5-30) } ; ; T = sqrt{ 107261.94 } = 327.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 327.51 }{ 26 } = 25.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 327.51 }{ 27 } = 24.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 327.51 }{ 30 } = 21.83 ; ;

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{ 26**2-27**2-30**2 }{ 2 * 27 * 30 } ) = 53° 57'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 57° 6'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-26**2-27**2 }{ 2 * 27 * 26 } ) = 68° 55'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 327.51 }{ 41.5 } = 7.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 53° 57'56" } = 16.08 ; ;




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