11 15 24 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 15   c = 24

Area: T = 59.1610797831
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 26.6277478393° = 26°37'39″ = 0.46547371695 rad
Angle ∠ C = γ = 134.1844385153° = 134°11'4″ = 2.34219593257 rad

Height: ha = 10.75765086965
Height: hb = 7.88881063775
Height: hc = 4.93300664859

Median: ma = 19.24218814049
Median: mb = 17.09553209973
Median: mc = 5.38551648071

Inradius: r = 2.36664319132
Circumradius: R = 16.73440542436

Vertex coordinates: A[24; 0] B[0; 0] C[9.83333333333; 4.93300664859]
Centroid: CG[11.27877777778; 1.64333554953]
Coordinates of the circumscribed circle: U[12; -11.66331287153]
Coordinates of the inscribed circle: I[10; 2.36664319132]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 153.3732521607° = 153°22'21″ = 0.46547371695 rad
∠ C' = γ' = 45.81656148467° = 45°48'56″ = 2.34219593257 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 = 15 ; ; c = 24 ; ;

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

p = a+b+c = 11+15+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-11)(25-15)(25-24) } ; ; T = sqrt{ 3500 } = 59.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.16 }{ 11 } = 10.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.16 }{ 15 } = 7.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.16 }{ 24 } = 4.93 ; ;

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**2-15**2-24**2 }{ 2 * 15 * 24 } ) = 19° 11'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-24**2 }{ 2 * 11 * 24 } ) = 26° 37'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 134° 11'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.16 }{ 25 } = 2.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 19° 11'17" } = 16.73 ; ;




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