7 26 28 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 26   c = 28

Area: T = 89.79766452603
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 14.2821970741° = 14°16'55″ = 0.24992674131 rad
Angle ∠ B = β = 66.3989922328° = 66°23'24″ = 1.15987227348 rad
Angle ∠ C = γ = 99.3288106931° = 99°19'41″ = 1.73436025057 rad

Height: ha = 25.65661843601
Height: hb = 6.90774342508
Height: hc = 6.414404609

Median: ma = 26.79108566492
Median: mb = 15.73221327226
Median: mc = 12.90334879006

Inradius: r = 2.94441523036
Circumradius: R = 14.18876124248

Vertex coordinates: A[28; 0] B[0; 0] C[2.80435714286; 6.414404609]
Centroid: CG[10.26878571429; 2.13880153633]
Coordinates of the circumscribed circle: U[14; -2.32996404754]
Coordinates of the inscribed circle: I[4.5; 2.94441523036]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.7188029259° = 165°43'5″ = 0.24992674131 rad
∠ B' = β' = 113.6110077672° = 113°36'36″ = 1.15987227348 rad
∠ C' = γ' = 80.6721893069° = 80°40'19″ = 1.73436025057 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 = 28 ; ;

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

p = a+b+c = 7+26+28 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-7)(30.5-26)(30.5-28) } ; ; T = sqrt{ 8063.44 } = 89.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 89.8 }{ 7 } = 25.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 89.8 }{ 26 } = 6.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 89.8 }{ 28 } = 6.41 ; ;

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**2-28**2 }{ 2 * 26 * 28 } ) = 14° 16'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-7**2-28**2 }{ 2 * 7 * 28 } ) = 66° 23'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-7**2-26**2 }{ 2 * 26 * 7 } ) = 99° 19'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 89.8 }{ 30.5 } = 2.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 16'55" } = 14.19 ; ;




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