6 26 29 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 26   c = 29

Area: T = 71.0210683607
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 10.85884782286° = 10°51'31″ = 0.19895161968 rad
Angle ∠ B = β = 54.71990522364° = 54°43'9″ = 0.95550276251 rad
Angle ∠ C = γ = 114.4222469535° = 114°25'21″ = 1.99770488316 rad

Height: ha = 23.67435612023
Height: hb = 5.46331295082
Height: hc = 4.89879781798

Median: ma = 27.3776997644
Median: mb = 16.41664551594
Median: mc = 12.07326964676

Inradius: r = 2.32985470035
Circumradius: R = 15.92549382371

Vertex coordinates: A[29; 0] B[0; 0] C[3.46655172414; 4.89879781798]
Centroid: CG[10.82218390805; 1.63326593933]
Coordinates of the circumscribed circle: U[14.5; -6.58443494634]
Coordinates of the inscribed circle: I[4.5; 2.32985470035]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.1421521771° = 169°8'29″ = 0.19895161968 rad
∠ B' = β' = 125.2810947764° = 125°16'51″ = 0.95550276251 rad
∠ C' = γ' = 65.5787530465° = 65°34'39″ = 1.99770488316 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 = 6 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 6+26+29 = 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 * (30.5-6)(30.5-26)(30.5-29) } ; ; T = sqrt{ 5043.94 } = 71.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.02 }{ 6 } = 23.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.02 }{ 26 } = 5.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.02 }{ 29 } = 4.9 ; ;

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{ 6**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 10° 51'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-6**2-29**2 }{ 2 * 6 * 29 } ) = 54° 43'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-6**2-26**2 }{ 2 * 26 * 6 } ) = 114° 25'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.02 }{ 30.5 } = 2.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 10° 51'31" } = 15.92 ; ;




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