10 26 30 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 26   c = 30

Area: T = 126.2549752475
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 18.88878819509° = 18°53'16″ = 0.33296557288 rad
Angle ∠ B = β = 57.31663611537° = 57°18'59″ = 11.0003592174 rad
Angle ∠ C = γ = 103.7965756895° = 103°47'45″ = 1.81215777074 rad

Height: ha = 25.2549950495
Height: hb = 9.71215194212
Height: hc = 8.4176650165

Median: ma = 27.62224546339
Median: mb = 18.19334053987
Median: mc = 12.76771453348

Inradius: r = 3.8265750075
Circumradius: R = 15.4465574837

Vertex coordinates: A[30; 0] B[0; 0] C[5.4; 8.4176650165]
Centroid: CG[11.8; 2.8065550055]
Coordinates of the circumscribed circle: U[15; -3.6833175538]
Coordinates of the inscribed circle: I[7; 3.8265750075]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.1122118049° = 161°6'44″ = 0.33296557288 rad
∠ B' = β' = 122.6843638846° = 122°41'1″ = 11.0003592174 rad
∠ C' = γ' = 76.20442431047° = 76°12'15″ = 1.81215777074 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 = 10 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 10+26+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-10)(33-26)(33-30) } ; ; T = sqrt{ 15939 } = 126.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 126.25 }{ 10 } = 25.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 126.25 }{ 26 } = 9.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 126.25 }{ 30 } = 8.42 ; ;

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{ 10**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 18° 53'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-10**2-30**2 }{ 2 * 10 * 30 } ) = 57° 18'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-10**2-26**2 }{ 2 * 26 * 10 } ) = 103° 47'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 126.25 }{ 33 } = 3.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 18° 53'16" } = 15.45 ; ;




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