11 26 28 triangle

Acute scalene triangle.

Sides: a = 11   b = 26   c = 28

Area: T = 142.9633063412
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 23.12660741872° = 23°7'34″ = 0.40436261376 rad
Angle ∠ B = β = 68.1766214748° = 68°10'34″ = 1.19898994189 rad
Angle ∠ C = γ = 88.69877110648° = 88°41'52″ = 1.54880670971 rad

Height: ha = 25.99332842566
Height: hb = 10.9977158724
Height: hc = 10.21216473865

Median: ma = 26.45327881328
Median: mb = 16.83774582405
Median: mc = 14.23302494708

Inradius: r = 4.39988634896
Circumradius: R = 14.00436171038

Vertex coordinates: A[28; 0] B[0; 0] C[4.08992857143; 10.21216473865]
Centroid: CG[10.69664285714; 3.40438824622]
Coordinates of the circumscribed circle: U[14; 0.31882640251]
Coordinates of the inscribed circle: I[6.5; 4.39988634896]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.8743925813° = 156°52'26″ = 0.40436261376 rad
∠ B' = β' = 111.8243785252° = 111°49'26″ = 1.19898994189 rad
∠ C' = γ' = 91.30222889352° = 91°18'8″ = 1.54880670971 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 = 11 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 11+26+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-11)(32.5-26)(32.5-28) } ; ; T = sqrt{ 20438.44 } = 142.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 142.96 }{ 11 } = 25.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 142.96 }{ 26 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 142.96 }{ 28 } = 10.21 ; ;

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{ 11**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 23° 7'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 68° 10'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-26**2 }{ 2 * 26 * 11 } ) = 88° 41'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 142.96 }{ 32.5 } = 4.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 7'34" } = 14 ; ;




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