11 24 30 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 24   c = 30

Area: T = 121.8544164886
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 19.78545253448° = 19°47'4″ = 0.34553051082 rad
Angle ∠ B = β = 47.60546523044° = 47°36'17″ = 0.8310857922 rad
Angle ∠ C = γ = 112.6110822351° = 112°36'39″ = 1.96554296234 rad

Height: ha = 22.15553027065
Height: hb = 10.15545137405
Height: hc = 8.12436109924

Median: ma = 26.60435711888
Median: mb = 19.14441897191
Median: mc = 11.11330553854

Inradius: r = 3.74993589196
Circumradius: R = 16.24989316788

Vertex coordinates: A[30; 0] B[0; 0] C[7.41766666667; 8.12436109924]
Centroid: CG[12.47222222222; 2.70878703308]
Coordinates of the circumscribed circle: U[15; -6.24772218386]
Coordinates of the inscribed circle: I[8.5; 3.74993589196]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.2155474655° = 160°12'56″ = 0.34553051082 rad
∠ B' = β' = 132.3955347696° = 132°23'43″ = 0.8310857922 rad
∠ C' = γ' = 67.38991776492° = 67°23'21″ = 1.96554296234 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 = 24 ; ; c = 30 ; ;

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

p = a+b+c = 11+24+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 * (32.5-11)(32.5-24)(32.5-30) } ; ; T = sqrt{ 14848.44 } = 121.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 121.85 }{ 11 } = 22.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 121.85 }{ 24 } = 10.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 121.85 }{ 30 } = 8.12 ; ;

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**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 19° 47'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-11**2-30**2 }{ 2 * 11 * 30 } ) = 47° 36'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-11**2-24**2 }{ 2 * 24 * 11 } ) = 112° 36'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 121.85 }{ 32.5 } = 3.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 19° 47'4" } = 16.25 ; ;




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