11 18 24 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 18   c = 24

Area: T = 93.4266107165
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 25.62881180847° = 25°37'41″ = 0.44772950417 rad
Angle ∠ B = β = 45.05440518787° = 45°3'15″ = 0.78663415466 rad
Angle ∠ C = γ = 109.3187830037° = 109°19'4″ = 1.90879560653 rad

Height: ha = 16.98765649391
Height: hb = 10.38106785739
Height: hc = 7.78655089304

Median: ma = 20.48878012485
Median: mb = 16.35554272338
Median: mc = 8.86600225733

Inradius: r = 3.52655134779
Circumradius: R = 12.71659317245

Vertex coordinates: A[24; 0] B[0; 0] C[7.77108333333; 7.78655089304]
Centroid: CG[10.59902777778; 2.59551696435]
Coordinates of the circumscribed circle: U[12; -4.20765329695]
Coordinates of the inscribed circle: I[8.5; 3.52655134779]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.3721881915° = 154°22'19″ = 0.44772950417 rad
∠ B' = β' = 134.9465948121° = 134°56'45″ = 0.78663415466 rad
∠ C' = γ' = 70.68221699634° = 70°40'56″ = 1.90879560653 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 = 24 ; ;

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

p = a+b+c = 11+18+24 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-11)(26.5-18)(26.5-24) } ; ; T = sqrt{ 8728.44 } = 93.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.43 }{ 11 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.43 }{ 18 } = 10.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.43 }{ 24 } = 7.79 ; ;

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**2-24**2 }{ 2 * 18 * 24 } ) = 25° 37'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-11**2-24**2 }{ 2 * 11 * 24 } ) = 45° 3'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-11**2-18**2 }{ 2 * 18 * 11 } ) = 109° 19'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.43 }{ 26.5 } = 3.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 25° 37'41" } = 12.72 ; ;




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