7 26 30 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 26   c = 30

Area: T = 79.79330918062
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 11.80659481286° = 11°48'21″ = 0.20660526662 rad
Angle ∠ B = β = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ C = γ = 118.7365653745° = 118°44'8″ = 2.07223280974 rad

Height: ha = 22.79880262304
Height: hb = 6.13879301389
Height: hc = 5.32195394537

Median: ma = 27.85222889544
Median: mb = 17.47985582929
Median: mc = 11.72660393996

Inradius: r = 2.53331140256
Circumradius: R = 17.1076744069

Vertex coordinates: A[30; 0] B[0; 0] C[4.55; 5.32195394537]
Centroid: CG[11.51766666667; 1.77331798179]
Coordinates of the circumscribed circle: U[15; -8.2244396187]
Coordinates of the inscribed circle: I[5.5; 2.53331140256]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.1944051871° = 168°11'39″ = 0.20660526662 rad
∠ B' = β' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ C' = γ' = 61.26443462551° = 61°15'52″ = 2.07223280974 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 = 26 ; ; c = 30 ; ;

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

p = a+b+c = 7+26+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-7)(31.5-26)(31.5-30) } ; ; T = sqrt{ 6366.94 } = 79.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.79 }{ 7 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.79 }{ 26 } = 6.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.79 }{ 30 } = 5.32 ; ;

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{ 7**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 11° 48'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-7**2-30**2 }{ 2 * 7 * 30 } ) = 49° 27'30" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-7**2-26**2 }{ 2 * 26 * 7 } ) = 118° 44'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.79 }{ 31.5 } = 2.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 11° 48'21" } = 17.11 ; ;




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