22 26 28 triangle

Acute scalene triangle.

Sides: a = 22   b = 26   c = 28

Area: T = 270.1111088258
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 47.90774859842° = 47°54'27″ = 0.83661433668 rad
Angle ∠ B = β = 61.28106643991° = 61°16'50″ = 1.07695493616 rad
Angle ∠ C = γ = 70.81218496167° = 70°48'43″ = 1.23658999252 rad

Height: ha = 24.5565553478
Height: hb = 20.77877760199
Height: hc = 19.29436491613

Median: ma = 24.67879253585
Median: mb = 21.56438586528
Median: mc = 19.59659179423

Inradius: r = 7.10881865331
Circumradius: R = 14.82435306659

Vertex coordinates: A[28; 0] B[0; 0] C[10.57114285714; 19.29436491613]
Centroid: CG[12.85771428571; 6.43112163871]
Coordinates of the circumscribed circle: U[14; 4.87220695196]
Coordinates of the inscribed circle: I[12; 7.10881865331]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.0932514016° = 132°5'33″ = 0.83661433668 rad
∠ B' = β' = 118.7199335601° = 118°43'10″ = 1.07695493616 rad
∠ C' = γ' = 109.1888150383° = 109°11'17″ = 1.23658999252 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 = 22 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 22+26+28 = 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 * (38-22)(38-26)(38-28) } ; ; T = sqrt{ 72960 } = 270.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 270.11 }{ 22 } = 24.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 270.11 }{ 26 } = 20.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 270.11 }{ 28 } = 19.29 ; ;

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{ 22**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 47° 54'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 61° 16'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-22**2-26**2 }{ 2 * 26 * 22 } ) = 70° 48'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 270.11 }{ 38 } = 7.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 47° 54'27" } = 14.82 ; ;




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