11 14 20 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 14   c = 20

Area: T = 74.15114497498
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 31.98220267884° = 31°58'55″ = 0.55881916689 rad
Angle ∠ B = β = 42.38546161308° = 42°23'5″ = 0.74397511037 rad
Angle ∠ C = γ = 105.6333357081° = 105°38' = 1.8443649881 rad

Height: ha = 13.48220817727
Height: hb = 10.593306425
Height: hc = 7.4155144975

Median: ma = 16.3633068172
Median: mb = 14.54330395722
Median: mc = 7.64985292704

Inradius: r = 3.29656199889
Circumradius: R = 10.38441530084

Vertex coordinates: A[20; 0] B[0; 0] C[8.125; 7.4155144975]
Centroid: CG[9.375; 2.47217149917]
Coordinates of the circumscribed circle: U[10; -2.79883269471]
Coordinates of the inscribed circle: I[8.5; 3.29656199889]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.0187973212° = 148°1'5″ = 0.55881916689 rad
∠ B' = β' = 137.6155383869° = 137°36'55″ = 0.74397511037 rad
∠ C' = γ' = 74.36766429192° = 74°22' = 1.8443649881 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 = 14 ; ; c = 20 ; ;

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

p = a+b+c = 11+14+20 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-11)(22.5-14)(22.5-20) } ; ; T = sqrt{ 5498.44 } = 74.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.15 }{ 11 } = 13.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.15 }{ 14 } = 10.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.15 }{ 20 } = 7.42 ; ;

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**2-14**2-20**2 }{ 2 * 14 * 20 } ) = 31° 58'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-11**2-20**2 }{ 2 * 11 * 20 } ) = 42° 23'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-11**2-14**2 }{ 2 * 14 * 11 } ) = 105° 38' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.15 }{ 22.5 } = 3.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 31° 58'55" } = 10.38 ; ;




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