4 11 14 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 11   c = 14

Area: T = 16.32329133429
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 12.23987557679° = 12°14'20″ = 0.21436065845 rad
Angle ∠ B = β = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ C = γ = 132.1022156536° = 132°6'8″ = 2.30656175805 rad

Height: ha = 8.16114566715
Height: hb = 2.9687802426
Height: hc = 2.33218447633

Median: ma = 12.43298028947
Median: mb = 8.70334475928
Median: mc = 4.41658804332

Inradius: r = 1.12657181616
Circumradius: R = 9.43545903066

Vertex coordinates: A[14; 0] B[0; 0] C[3.25; 2.33218447633]
Centroid: CG[5.75; 0.77772815878]
Coordinates of the circumscribed circle: U[7; -6.32554639555]
Coordinates of the inscribed circle: I[3.5; 1.12657181616]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.7611244232° = 167°45'40″ = 0.21436065845 rad
∠ B' = β' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ C' = γ' = 47.89878434641° = 47°53'52″ = 2.30656175805 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 = 4 ; ; b = 11 ; ; c = 14 ; ;

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

p = a+b+c = 4+11+14 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-4)(14.5-11)(14.5-14) } ; ; T = sqrt{ 266.44 } = 16.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.32 }{ 4 } = 8.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.32 }{ 11 } = 2.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.32 }{ 14 } = 2.33 ; ;

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{ 4**2-11**2-14**2 }{ 2 * 11 * 14 } ) = 12° 14'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-4**2-14**2 }{ 2 * 4 * 14 } ) = 35° 39'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-4**2-11**2 }{ 2 * 11 * 4 } ) = 132° 6'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.32 }{ 14.5 } = 1.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 12° 14'20" } = 9.43 ; ;




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