9 26 30 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 26   c = 30

Area: T = 111.4044387257
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 16.59878421359° = 16°35'52″ = 0.2989686994 rad
Angle ∠ B = β = 55.61105672911° = 55°36'38″ = 0.97105874981 rad
Angle ∠ C = γ = 107.7921590573° = 107°47'30″ = 1.88113181615 rad

Height: ha = 24.75765305014
Height: hb = 8.57695682505
Height: hc = 7.42769591504

Median: ma = 27.7088302005
Median: mb = 17.9330421077
Median: mc = 12.39895116934

Inradius: r = 3.42878273002
Circumradius: R = 15.75334190818

Vertex coordinates: A[30; 0] B[0; 0] C[5.08333333333; 7.42769591504]
Centroid: CG[11.69444444444; 2.47656530501]
Coordinates of the circumscribed circle: U[15; -4.81435447194]
Coordinates of the inscribed circle: I[6.5; 3.42878273002]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.4022157864° = 163°24'8″ = 0.2989686994 rad
∠ B' = β' = 124.3899432709° = 124°23'22″ = 0.97105874981 rad
∠ C' = γ' = 72.2088409427° = 72°12'30″ = 1.88113181615 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 = 9 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 9+26+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-9)(32.5-26)(32.5-30) } ; ; T = sqrt{ 12410.94 } = 111.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 111.4 }{ 9 } = 24.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 111.4 }{ 26 } = 8.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 111.4 }{ 30 } = 7.43 ; ;

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{ 9**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 16° 35'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-9**2-30**2 }{ 2 * 9 * 30 } ) = 55° 36'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-9**2-26**2 }{ 2 * 26 * 9 } ) = 107° 47'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 111.4 }{ 32.5 } = 3.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 16° 35'52" } = 15.75 ; ;




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