11 26 30 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 26   c = 30

Area: T = 140.6622495001
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 21.14215369426° = 21°8'30″ = 0.36989894286 rad
Angle ∠ B = β = 58.48546299979° = 58°29'5″ = 1.02107493553 rad
Angle ∠ C = γ = 100.3743833059° = 100°22'26″ = 1.75218538697 rad

Height: ha = 25.57549990912
Height: hb = 10.82201919232
Height: hc = 9.37774996668

Median: ma = 27.5277259217
Median: mb = 18.48797186126
Median: mc = 13.17219398723

Inradius: r = 4.19988804478
Circumradius: R = 15.24992674041

Vertex coordinates: A[30; 0] B[0; 0] C[5.75; 9.37774996668]
Centroid: CG[11.91766666667; 3.12658332223]
Coordinates of the circumscribed circle: U[15; -2.74659345151]
Coordinates of the inscribed circle: I[7.5; 4.19988804478]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8588463057° = 158°51'30″ = 0.36989894286 rad
∠ B' = β' = 121.5155370002° = 121°30'55″ = 1.02107493553 rad
∠ C' = γ' = 79.62661669405° = 79°37'34″ = 1.75218538697 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 = 11 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 11+26+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-11)(33.5-26)(33.5-30) } ; ; T = sqrt{ 19785.94 } = 140.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 140.66 }{ 11 } = 25.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 140.66 }{ 26 } = 10.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 140.66 }{ 30 } = 9.38 ; ;

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{ 11**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 21° 8'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-11**2-30**2 }{ 2 * 11 * 30 } ) = 58° 29'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-11**2-26**2 }{ 2 * 26 * 11 } ) = 100° 22'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 140.66 }{ 33.5 } = 4.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 8'30" } = 15.25 ; ;




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