10 21 26 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 21   c = 26

Area: T = 99.42880518767
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 21.35986848161° = 21°21'31″ = 0.37327793739 rad
Angle ∠ B = β = 49.89219743369° = 49°53'31″ = 0.87107792225 rad
Angle ∠ C = γ = 108.7499340847° = 108°44'58″ = 1.89880340572 rad

Height: ha = 19.88656103753
Height: hb = 9.4699338274
Height: hc = 7.64883116828

Median: ma = 23.09876189249
Median: mb = 16.66658333125
Median: mc = 10.07547208398

Inradius: r = 3.48987035746
Circumradius: R = 13.72985200126

Vertex coordinates: A[26; 0] B[0; 0] C[6.44223076923; 7.64883116828]
Centroid: CG[10.81441025641; 2.54994372276]
Coordinates of the circumscribed circle: U[13; -4.41327385755]
Coordinates of the inscribed circle: I[7.5; 3.48987035746]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.6411315184° = 158°38'29″ = 0.37327793739 rad
∠ B' = β' = 130.1088025663° = 130°6'29″ = 0.87107792225 rad
∠ C' = γ' = 71.2510659153° = 71°15'2″ = 1.89880340572 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 = 21 ; ; c = 26 ; ;

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

p = a+b+c = 10+21+26 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-10)(28.5-21)(28.5-26) } ; ; T = sqrt{ 9885.94 } = 99.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 99.43 }{ 10 } = 19.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 99.43 }{ 21 } = 9.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 99.43 }{ 26 } = 7.65 ; ;

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**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 21° 21'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 49° 53'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-21**2 }{ 2 * 21 * 10 } ) = 108° 44'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 99.43 }{ 28.5 } = 3.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 21° 21'31" } = 13.73 ; ;




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