4 26 28 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 26   c = 28

Area: T = 46.63768952654
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 7.36111606635° = 7°21'40″ = 0.12884764903 rad
Angle ∠ B = β = 56.38876254015° = 56°23'15″ = 0.98441497206 rad
Angle ∠ C = γ = 116.2511213935° = 116°15'4″ = 2.02989664426 rad

Height: ha = 23.31884476327
Height: hb = 3.5877453482
Height: hc = 3.33112068047

Median: ma = 26.94443871706
Median: mb = 15.19986841536
Median: mc = 12.24774487139

Inradius: r = 1.60881688023
Circumradius: R = 15.61099585072

Vertex coordinates: A[28; 0] B[0; 0] C[2.21442857143; 3.33112068047]
Centroid: CG[10.07114285714; 1.11104022682]
Coordinates of the circumscribed circle: U[14; -6.90444047244]
Coordinates of the inscribed circle: I[3; 1.60881688023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.6398839336° = 172°38'20″ = 0.12884764903 rad
∠ B' = β' = 123.6122374598° = 123°36'45″ = 0.98441497206 rad
∠ C' = γ' = 63.7498786065° = 63°44'56″ = 2.02989664426 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 = 4 ; ; b = 26 ; ; c = 28 ; ;

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

p = a+b+c = 4+26+28 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-4)(29-26)(29-28) } ; ; T = sqrt{ 2175 } = 46.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.64 }{ 4 } = 23.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.64 }{ 26 } = 3.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.64 }{ 28 } = 3.33 ; ;

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{ 4**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 7° 21'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-4**2-28**2 }{ 2 * 4 * 28 } ) = 56° 23'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-4**2-26**2 }{ 2 * 26 * 4 } ) = 116° 15'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.64 }{ 29 } = 1.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 7° 21'40" } = 15.61 ; ;




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