11 18 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 18   c = 28

Area: T = 51.17106703102
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 11.71658523949° = 11°42'57″ = 0.2044480199 rad
Angle ∠ B = β = 19.40770433824° = 19°24'25″ = 0.33987168051 rad
Angle ∠ C = γ = 148.8777104223° = 148°52'38″ = 2.59883956495 rad

Height: ha = 9.30437582382
Height: hb = 5.68656300345
Height: hc = 3.65550478793

Median: ma = 22.88655849827
Median: mb = 19.27443352674
Median: mc = 5.14878150705

Inradius: r = 1.79554621161
Circumradius: R = 27.0865828495

Vertex coordinates: A[28; 0] B[0; 0] C[10.375; 3.65550478793]
Centroid: CG[12.79216666667; 1.21883492931]
Coordinates of the circumscribed circle: U[14; -23.18771107571]
Coordinates of the inscribed circle: I[10.5; 1.79554621161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2844147605° = 168°17'3″ = 0.2044480199 rad
∠ B' = β' = 160.5932956618° = 160°35'35″ = 0.33987168051 rad
∠ C' = γ' = 31.12328957773° = 31°7'22″ = 2.59883956495 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 = 18 ; ; c = 28 ; ;

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

p = a+b+c = 11+18+28 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-11)(28.5-18)(28.5-28) } ; ; T = sqrt{ 2618.44 } = 51.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.17 }{ 11 } = 9.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.17 }{ 18 } = 5.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.17 }{ 28 } = 3.66 ; ;

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**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 11° 42'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 19° 24'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-18**2 }{ 2 * 18 * 11 } ) = 148° 52'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.17 }{ 28.5 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 11° 42'57" } = 27.09 ; ;




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