4 24 26 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 24   c = 26

Area: T = 43.16224837098
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 7.95218754307° = 7°57'7″ = 0.1398786408 rad
Angle ∠ B = β = 56.1043644797° = 56°6'13″ = 0.97991933241 rad
Angle ∠ C = γ = 115.9444479772° = 115°56'40″ = 2.02436129215 rad

Height: ha = 21.58112418549
Height: hb = 3.59768736425
Height: hc = 3.32201910546

Median: ma = 24.94399278267
Median: mb = 14.21326704036
Median: mc = 11.26994276696

Inradius: r = 1.59986105078
Circumradius: R = 14.45769993746

Vertex coordinates: A[26; 0] B[0; 0] C[2.23107692308; 3.32201910546]
Centroid: CG[9.41102564103; 1.10767303515]
Coordinates of the circumscribed circle: U[13; -6.32549372264]
Coordinates of the inscribed circle: I[3; 1.59986105078]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.0488124569° = 172°2'53″ = 0.1398786408 rad
∠ B' = β' = 123.8966355203° = 123°53'47″ = 0.97991933241 rad
∠ C' = γ' = 64.05655202276° = 64°3'20″ = 2.02436129215 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 = 24 ; ; c = 26 ; ;

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

p = a+b+c = 4+24+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-4)(27-24)(27-26) } ; ; T = sqrt{ 1863 } = 43.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.16 }{ 4 } = 21.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.16 }{ 24 } = 3.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.16 }{ 26 } = 3.32 ; ;

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**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 7° 57'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-4**2-26**2 }{ 2 * 4 * 26 } ) = 56° 6'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-4**2-24**2 }{ 2 * 24 * 4 } ) = 115° 56'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.16 }{ 27 } = 1.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 7° 57'7" } = 14.46 ; ;




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