20 26 28 triangle

Acute scalene triangle.

Sides: a = 20   b = 26   c = 28

Area: T = 249.5421579702
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 43.27991752006° = 43°16'45″ = 0.75553641048 rad
Angle ∠ B = β = 63.02769449584° = 63°1'37″ = 1.1100027707 rad
Angle ∠ C = γ = 73.6943879841° = 73°41'38″ = 1.28662008418 rad

Height: ha = 24.95441579702
Height: hb = 19.19655061309
Height: hc = 17.82443985501

Median: ma = 25.1099800796
Median: mb = 20.56769638012
Median: mc = 18.49332420089

Inradius: r = 6.7444367019
Circumradius: R = 14.58767474445

Vertex coordinates: A[28; 0] B[0; 0] C[9.07114285714; 17.82443985501]
Centroid: CG[12.35771428571; 5.94114661834]
Coordinates of the circumscribed circle: U[14; 4.09655098594]
Coordinates of the inscribed circle: I[11; 6.7444367019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.7210824799° = 136°43'15″ = 0.75553641048 rad
∠ B' = β' = 116.9733055042° = 116°58'23″ = 1.1100027707 rad
∠ C' = γ' = 106.3066120159° = 106°18'22″ = 1.28662008418 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 = 28 ; ;

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

p = a+b+c = 20+26+28 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-20)(37-26)(37-28) } ; ; T = sqrt{ 62271 } = 249.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 249.54 }{ 20 } = 24.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 249.54 }{ 26 } = 19.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 249.54 }{ 28 } = 17.82 ; ;

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{ 20**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 43° 16'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-20**2-28**2 }{ 2 * 20 * 28 } ) = 63° 1'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-20**2-26**2 }{ 2 * 26 * 20 } ) = 73° 41'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 249.54 }{ 37 } = 6.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 43° 16'45" } = 14.59 ; ;




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