7 21 26 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 21   c = 26

Area: T = 56.9210997883
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 12.03545697281° = 12°2'4″ = 0.21100428658 rad
Angle ∠ B = β = 38.71992973222° = 38°43'9″ = 0.67657792223 rad
Angle ∠ C = γ = 129.246613295° = 129°14'46″ = 2.25657705654 rad

Height: ha = 16.26331422523
Height: hb = 5.42110474174
Height: hc = 4.37985382987

Median: ma = 23.3721991785
Median: mb = 15.88223801743
Median: mc = 8.71877978871

Inradius: r = 2.10881851068
Circumradius: R = 16.78664239127

Vertex coordinates: A[26; 0] B[0; 0] C[5.46215384615; 4.37985382987]
Centroid: CG[10.48771794872; 1.46595127662]
Coordinates of the circumscribed circle: U[13; -10.62199824754]
Coordinates of the inscribed circle: I[6; 2.10881851068]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.9655430272° = 167°57'56″ = 0.21100428658 rad
∠ B' = β' = 141.2810702678° = 141°16'51″ = 0.67657792223 rad
∠ C' = γ' = 50.75438670503° = 50°45'14″ = 2.25657705654 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 = 7 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 7+21+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 * (27-7)(27-21)(27-26) } ; ; T = sqrt{ 3240 } = 56.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 56.92 }{ 7 } = 16.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 56.92 }{ 21 } = 5.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 56.92 }{ 26 } = 4.38 ; ;

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{ 7**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 12° 2'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-7**2-26**2 }{ 2 * 7 * 26 } ) = 38° 43'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-7**2-21**2 }{ 2 * 21 * 7 } ) = 129° 14'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 56.92 }{ 27 } = 2.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 12° 2'4" } = 16.79 ; ;




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